# questions

tags: ['Mathematics', 'Sets and Relations', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch2_P1.db
title:
let-mathrmax-x-in-mathrmrx-1-mathrmbx-x-in-mathrmrx1-geq-1-text-and-mathrma-cup-mathrmbmathrmrmathrmd-text-then-the-set-mathrmd-is

slug:
let-mathrmax-x-in-mathrmrx-1-mathrmbx-x-in-mathrmrx1-geq-1-text-and-mathrma-cup-mathrmbmathrmrmathrmd-text-then-the-set-mathrmd-is-20031

question:
<div class="question">Let \(\mathrm{A}=\{x: x \in \mathrm{R},|x|  &lt; 1\}\);<br/>\(\mathrm{B}=\{x: x \in \mathrm{R},|x-1| \geq 1\} \text { and } \mathrm{A} \cup \mathrm{B}=\mathrm{R}-\mathrm{D} \text {, }\)<br/>then the set \(\mathrm{D}\) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\{x: 1  &lt; x \leq 2\}\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(\{x: 1 \leq x  &lt; 2\}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\{x: 1 \leq x \leq 2\}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\{x: 1 \leq x  &lt; 2\}\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \mathrm{A}=[x: x \in \mathrm{R},-1  &lt; x &lt; 1] \\<br/>&amp; \mathrm{B}=[x: x \in \mathrm{R}: x-1 \leq-1 \text { or } x-1 \geq 1] \\<br/>&amp;=[x: x \in R: x \leq 0 \text { or } x \geq 2] \\<br/>&amp; \therefore A \cup B=R-D,<br/>\end{aligned}\)<br/>where \(D=[x: x \in R, 1 \leq x &lt; 2]\)</div>


title: let-mathrmfmathrmx-leftbeginarrayla-x21-x-1-xa-x-leq-1endarrayright-then-fx-is-derivable-at-x1-if
tags: ['Mathematics', 'Application of Derivatives', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch2_P1.db
slug:
let-mathrmfmathrmx-leftbeginarrayla-x21-x-1-xa-x-leq-1endarrayright-then-fx-is-derivable-at-x1-if-21298

question:
<div class="question">Let \(\mathrm{f}(\mathrm{x})=\) \(\left\{\begin{array}{l}a x^2+1, x &gt; 1 \\ x+a, x \leq 1\end{array}\right.\). Then \(f(x)\) is derivable at \(x=1\), if</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(a=2\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(a=1\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(a=0\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">\(a=1 / 2\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(a=1 / 2\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \operatorname{Lf}^{\prime}(1)=\lim _{h \rightarrow 0} \frac{f(1-h)-f(1)}{-h} \\<br/>&amp; =\lim _{h \rightarrow 0} \frac{(1-h+a)-(1+a)}{-h}=\lim _{h \rightarrow 0} \frac{-h}{-h}=1 \\<br/>&amp; \operatorname{Rf}^{\prime}(1)=\lim _{h \rightarrow 0} \frac{f(1+h)-f(1)}{h} \\<br/>&amp; =\lim _{h \rightarrow 0} \frac{\left[a(1+h)^2+1\right]-(1+a)}{h} \\<br/>&amp; =\lim _{h \rightarrow 0}(a h+2 a)=2 a<br/>\end{aligned}\)<br/>Since f' (1) exists, \(\therefore L f^{\prime}(1)=R f^{\prime}(1) \Rightarrow a=1 / 2\)</div>


title: let-mathrmi1int12-frac1sqrt1mathrmx2-mathrmdx-and-mathrmi2int12-frac1x-d-x-then
slug: let-mathrmi1int12-frac1sqrt1mathrmx2-mathrmdx-and-mathrmi2int12-frac1x-d-x-then-72094
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch2_P1.db
question:
<div class="question">Let \(\mathrm{I}_1=\int_1^2 \frac{1}{\sqrt{1+\mathrm{x}^2}} \mathrm{dx}\) and \(\mathrm{I}_2=\int_1^2 \frac{1}{x} d x\), then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\mathrm{I}_1 &gt; \mathrm{I}_2\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(\mathrm{I}_2 &gt; \mathrm{I}_1\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\mathrm{I}_1=\mathrm{I}_2\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\mathrm{I}_2 &gt; \mathrm{I}_1\)</span> </div>

answer:
<div class="solution">If \(I_1=\int_1^2 \frac{\mathrm{dx}}{\sqrt{1+\mathrm{x}^2}}, I_2=\int_1^2 \frac{\mathrm{dx}}{\mathrm{x}}\)<br/>\(I_1=\ell n \left(\frac{2+\sqrt{5}}{1+\sqrt{2}}\right), \quad I_2=\ell n 2 \Rightarrow I_1  &lt; I_2\)</div>


tags: ['Mathematics', 'Quadratic Equation', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch2_P2.db
title:
let-p-and-q-be-roots-of-the-equation-x-2-2-x-a-0-and-let-r-and-s-be-the-roots-of-the-equation-x-2-18-x-b-0-if-p-q-r-s-are-in-arithmetic-progression-th

slug:
let-p-and-q-be-roots-of-the-equation-x-2-2-x-a-0-and-let-r-and-s-be-the-roots-of-the-equation-x-2-18-x-b-0-if-p-q-r-s-are-in-arithmetic-progression-th-34670

question:
<div class="question">Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> be roots of the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mi>A</mi><mo>=</mo><mn>0</mn></math> and let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math> be the roots of the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mi>x</mi><mo>+</mo><mi>B</mi><mo>=</mo><mn>0</mn></math>. If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>&lt;</mo><mi>q</mi><mo>&lt;</mo><mi>r</mi><mo>&lt;</mo><mi>s</mi></math> are in arithmetic progression, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>77</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>77</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>77</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>77</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>77</mn></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mi>A</mi><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>x</mi><mo>=</mo><mn>1</mn><mo>±</mo><msqrt><mn>1</mn><mo>-</mo><mi>A</mi></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>p</mi><mo>=</mo><mn>1</mn><mo>-</mo><msqrt><mn>1</mn><mo>-</mo><mi>A</mi></msqrt><mo>,</mo><mi>q</mi><mo>=</mo><mn>1</mn><mo>+</mo><msqrt><mn>1</mn><mo>-</mo><mi>A</mi></msqrt></math></p><p>Similarly, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>9</mn><mo>-</mo><msqrt><mn>81</mn><mo>-</mo><mi>B</mi></msqrt><mo>,</mo><mi>s</mi><mo>=</mo><mn>9</mn><mo>+</mo><msqrt><mn>81</mn><mo>-</mo><mi>B</mi></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>s</mi></math> are in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AP</mi></math>.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mi>q</mi><mo>-</mo><mi>p</mi><mo>=</mo><mi>s</mi><mo>-</mo><mi>r</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mn>2</mn><msqrt><mn>1</mn><mo>-</mo><mi>A</mi></msqrt><mo>=</mo><mn>2</mn><msqrt><mn>81</mn><mo>-</mo><mi>B</mi></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>B</mi><mo>=</mo><mn>80</mn><mo>+</mo><mi>A</mi></math></p><p>and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>-</mo><mi>p</mi><mo>=</mo><mi>r</mi><mo>-</mo><mi>q</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mn>3</mn><msqrt><mn>1</mn><mo>-</mo><mi>A</mi></msqrt><mo>=</mo><mn>8</mn><mo>-</mo><msqrt><mn>81</mn><mo>-</mo><mi>B</mi></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>A</mi><mo>=</mo><mo>-</mo><mn>3</mn><mo>,</mo><mi>B</mi><mo>=</mo><mn>77</mn></math></p></div>


tags: ['Mathematics', 'Indefinite Integration', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P2.db
title:
let-p-x-d-x-e-x-8-e-x-4-e-3-x-q-x-d-x-e-3-x-8-e-x-4-e-x-and-r-x-p-x-2-q-x-if-r-x-1-2-a-b-2-e-x-c-k-then-the-value-of-a-b-c-is

slug:
let-p-x-d-x-e-x-8-e-x-4-e-3-x-q-x-d-x-e-3-x-8-e-x-4-e-x-and-r-x-p-x-2-q-x-if-r-x-1-2-a-b-2-e-x-c-k-then-the-value-of-a-b-c-is-34175

question:
<div class="question">Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>∫</mo><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><msup><mi>e</mi><mi>x</mi></msup><mo>+</mo><mn>8</mn><msup><mi>e</mi><mrow><mo>-</mo><mi>x</mi></mrow></msup><mo>+</mo><mn>4</mn><msup><mi>e</mi><mrow><mo>-</mo><mn>3</mn><mi>x</mi></mrow></msup></mrow></mfrac><mo>,</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>∫</mo><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><msup><mi>e</mi><mrow><mn>3</mn><mi>x</mi></mrow></msup><mo>+</mo><mn>8</mn><msup><mi>e</mi><mi>x</mi></msup><mo>+</mo><mn>4</mn><msup><mi>e</mi><mrow><mo>-</mo><mi>x</mi></mrow></msup></mrow></mfrac></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>P</mi><mfenced><mi>x</mi></mfenced><mo>-</mo><mn>2</mn><mi>Q</mi><mfenced><mi>x</mi></mfenced></math>. If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>A</mi><mfenced><mfrac><mrow><mi>B</mi><mo>+</mo><mn>2</mn><msup><mi>e</mi><mrow><mo>-</mo><mi>x</mi></mrow></msup></mrow><mi>C</mi></mfrac></mfenced><mo>+</mo><mi>K</mi><mo>,</mo></math> then the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi></mrow></mfenced></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mn>2</mn><mo>,</mo><msup><mi>e</mi><mi>x</mi></msup></mrow></mfenced></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><msup><mi>e</mi><mi>x</mi></msup><mo>,</mo><mn>2</mn></mrow></mfenced></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><msup><mi>e</mi><mi>x</mi></msup></mfrac></mrow></mfenced></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mfrac><mn>1</mn><msup><mi>e</mi><mi>x</mi></msup></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><msup><mi>e</mi><mi>x</mi></msup><mo>,</mo><mn>2</mn></mrow></mfenced></math></span> </div>

answer:
<div class="solution"><p>We have, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>∫</mo><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><msup><mi>e</mi><mi>x</mi></msup><mo>+</mo><mn>8</mn><msup><mi>e</mi><mrow><mo>-</mo><mi>x</mi></mrow></msup><mo>+</mo><mn>4</mn><msup><mi>e</mi><mrow><mo>-</mo><mn>3</mn><mi>x</mi></mrow></msup></mrow></mfrac><mo>-</mo><mn>2</mn><mo>∫</mo><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><msup><mi>e</mi><mrow><mn>3</mn><mi>x</mi></mrow></msup><mo>+</mo><mn>8</mn><msup><mi>e</mi><mi>x</mi></msup><mo>+</mo><mn>4</mn><msup><mi>e</mi><mrow><mo>-</mo><mi>x</mi></mrow></msup></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>R</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>∫</mo><mfrac><mrow><msup><mi>e</mi><mi>x</mi></msup><mfenced><mrow><msup><mi>e</mi><mrow><mn>2</mn><mi>x</mi></mrow></msup><mo>-</mo><mn>2</mn></mrow></mfenced></mrow><mrow><msup><mi>e</mi><mrow><mn>4</mn><mi>x</mi></mrow></msup><mo>+</mo><mn>8</mn><msup><mi>e</mi><mrow><mn>2</mn><mi>x</mi></mrow></msup><mo>+</mo><mn>4</mn></mrow></mfrac><mi>d</mi><mi>x</mi></math></p><p>we get <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mo>∫</mo><mfrac><mrow><mfenced><mrow><msup><mi>t</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn></mrow></mfenced><mi>d</mi><mi>t</mi></mrow><mrow><msup><mi>t</mi><mn>4</mn></msup><mo>+</mo><mn>8</mn><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mo>∫</mo><mfrac><mrow><mfenced><mrow><mn>1</mn><mo>-</mo><mn>2</mn><msup><mi>t</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced><mi>d</mi><mi>t</mi></mrow><mrow><msup><mfenced><mrow><mi>t</mi><mo>+</mo><mn>2</mn><msup><mi>t</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mi>t</mi><mo>+</mo><mn>2</mn><msup><mi>t</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mn>2</mn></mfrac></mfenced><mo>+</mo><mi>K</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>R</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><msup><mi>e</mi><mi>x</mi></msup><mo>+</mo><mn>2</mn><msup><mi>e</mi><mrow><mo>-</mo><mi>x</mi></mrow></msup></mrow><mn>2</mn></mfrac></mfenced><mo>+</mo><mi>K</mi></math></p><p>Hence, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi></mrow></mfenced><mo>=</mo><mfenced><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><msup><mi>e</mi><mi>x</mi></msup><mo>,</mo><mn>2</mn></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Option (b) is correct.</p></div>


title: let-r-3-3-6-6-9-9-12-12-6-12-3-9-3-12-3-6-be-a-relation-on-the-set-a-3-6-9-12-then-the-relation-is
tags: ['Mathematics', 'Sets and Relations', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P2.db
slug:
let-r-3-3-6-6-9-9-12-12-6-12-3-9-3-12-3-6-be-a-relation-on-the-set-a-3-6-9-12-then-the-relation-is-53344

question:
<div class="question">Let $R=\{(3,3),(6,6),(9,9),(12,12),(6,12), (3,9),(3,12),(3,6)$ be a relation on the set $A=\{3,6,9,12\}$. Then, the relation is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">an equivalence relation</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">reflexive and symmetric</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">reflexive and transitive</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">onlyreflexive</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">reflexive and transitive</span> </div>

answer:
<div class="solution">$(3,3),(6,6),(9,9),(12,12), \in R$.
<br/> <br/>$R$ isnot symmetricas (6,12)$\notin R$ but (12,6)$\in R$ $R$ is transitive as the only pair which needs verification is (3,6) and (6,12)$\in R$.
<br/> <br/>$$
<br/> <br/>\Rightarrow \quad(3,12) \in R
<br/> <br/>$$</div>


title: let-r-be-the-relation-on-the-set-r-of-all-real-numbers-defined-by-a-r-b-if-a-b-1-then-r-is
slug: let-r-be-the-relation-on-the-set-r-of-all-real-numbers-defined-by-a-r-b-if-a-b-1-then-r-is-23557
tags: ['Mathematics', 'Sets and Relations', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P2.db
question:
<div class="question">Let $R$ be the relation on the set $R$ of all real numbers, defined by $a R b$ If $|a-b| \leq 1$. Then, $R$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">reflexive and symmetric only</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">reflexive and transitive only</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">equivalence</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">reflexive and symmetric only</span> </div>

answer:
<div class="solution">Since, $|a-a|=0 \leq 1,$ so $a R a, \forall a \in R$ $\therefore R$ is reflexive. Now, $a R b \Rightarrow|a-b| \leq 1 \Rightarrow|b-a| \leq 1 \Rightarrow b R a$
<br/> <br/>$\therefore R$ is symmetric. But $R$ is not transitive as
<br/> <br/>$1 R 2,2 R 3$ but $1 \not R^{\prime} 3$
<br/> <br/>$$
<br/> <br/>[\because|1-3|=2&gt;1]
<br/> <br/>$$</div>


tags: ['Mathematics', 'Parabola', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P2.db
title:
let-s-be-the-focus-of-the-parabola-y-2-8-x-and-pq-be-the-common-chord-of-the-circle-x-2-y-2-2-x-4-y-0-and-the-given-parabola-the-area-of-pqs-is

slug:
let-s-be-the-focus-of-the-parabola-y-2-8-x-and-pq-be-the-common-chord-of-the-circle-x-2-y-2-2-x-4-y-0-and-the-given-parabola-the-area-of-pqs-is-13908

question:
<div class="question">Let $\mathrm{S}$ be the focus of the parabola $\mathrm{y}^{2}=8 \mathrm{x}$ and $\mathrm{PQ}$ be the common chord of the circle $\mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}-$ $4 y=0$ and the given parabola. The area of $\Delta P Q S$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$4 \mathrm{sq}$ units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 \mathrm{sq}$ units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2 sq units</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$8 s q$ units</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \mathrm{sq}$ units</span> </div>

answer:
<div class="solution">The parametric equations of the parabola $y^{2}=8 x$ are $x=2 t^{2}$ and $y=4 t$
<br/> <br/>and the given equation of circle is
<br/> <br/>$x^{2}+y^{2}-2 x-4 y=0$
<br/> <br/>On putting $x=2 t^{2}$ and $y=4$ t in circle
<br/> <br/>we get
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>4 t^{4}+16 t^{2}-4 t^{2}-16 t=0 \\
<br/> <br/>\Rightarrow 4 t^{2}+12 t^{2}-16 t=0 \\
<br/> <br/>\Rightarrow 4 t\left(t^{3}+3 t-4\right)=0 \\
<br/> <br/>\Rightarrow t(t-1)\left(t^{2}+t+4\right)=0 \\
<br/> <br/>\Rightarrow t=0, t=1 \\
<br/> <br/>\quad\left[\because t^{2}+t+4 \neq 0\right]
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Thus the coordinates of points of intersection of the circle and the parabola are $\mathrm{Q}(0,0)$ and $\mathrm{P}(2,4) .$ Clearly these are diametrically opposite points on the circle.
<br/> <br/>The coordinates of the focus $\mathrm{S}$ of the parabola are (2,0) which lies on the circle.
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>\therefore \text { Area of } \Delta \mathrm{PQS} &amp;=\frac{1}{2} \times \mathrm{QS} \times \mathrm{SP}=\frac{1}{2} \times 2 \times 4 \\
<br/> <br/>&amp;=4 \mathrm{sq} . \text { units. }
<br/> <br/>\end{aligned}
<br/> <br/>$$</div>


title: let-t-k-be-the-statement-1-3-5-2-k-1-k-2-10-which-of-the-following-is-correct
slug: let-t-k-be-the-statement-1-3-5-2-k-1-k-2-10-which-of-the-following-is-correct-47844
tags: ['Mathematics', 'Mathematical Induction', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P2.db
question:
<div class="question">Let $\mathrm{T}(k)$ be the statement $1+3+5+\ldots+$ $(2 k-1)=k^{2}+10$
<br/>Which of the following is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{T}(1)$ is true</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{T}(k)$ is true $\Rightarrow \mathrm{T}(k+1)$ is true</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{T}(n)$ is true for all $n \in \mathbf{N}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">All above are correct</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{T}(k)$ is true $\Rightarrow \mathrm{T}(k+1)$ is true</span> </div>

answer:
<div class="solution">When $\mathrm{k}=1, \mathrm{LHS}=1$ but $\mathrm{RHS}=1+10=11$
<br/>$\therefore \mathrm{T}(1)$ is not true Let $\mathrm{T}(k)$ is true. That is
<br/>$\begin{array}{l}
<br/>1+3+5+\ldots .+(2 k-1)=k^{2}+10 \\
<br/>\text { Now, } 1+3+5+\ldots . .+(2 k-1)+(2 k+1) \\
<br/>=k^{2}+10+2 k+1=(k+1)^{2}+10
<br/>\end{array}$
<br/>$\therefore \mathrm{T}(k+1)$ is true.
<br/>That is $\mathrm{T}(k)$ is true $\Rightarrow \mathrm{T}(k+1)$ is true.
<br/>But $\mathrm{T}(n)$ is not true for all $n \in \mathbf{N},$ as $\mathrm{T}(1)$ is not true.</div>


tags: ['Mathematics', 'Basic of Mathematics', 'BITSAT', 'BITSAT 2012']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P2.db
title:
let-x-and-y-be-two-natural-numbers-such-that-x-y-12-x-y-and-x-y-then-the-total-number-of-pairs-x-y-is

slug:
let-x-and-y-be-two-natural-numbers-such-that-x-y-12-x-y-and-x-y-then-the-total-number-of-pairs-x-y-is-48170

question:
<div class="question">Let $x$ and $y$ be two natural numbers such that $x y=12(x+y)$ and $x \leq y$. Then the total number of pairs $(x, y)$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">8</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">16</span> </li> </ul>

answer:
<div class="solution">$x y-12 x-12 y=0 \Rightarrow(x-12)(y-12)=144$
<br/>Now 144 can be factorised into two factors $x$ and $y$ where $x \leq y$ and the factors are (1,144),(2,72),(3,48),(4,36),(6,24),(8,18)
<br/>(9,16),(12,12)
<br/>Thus there are eight solutions.</div>


title: let-x-denote-the-greatest-integer-x-if-f-x-x-and-g-x-x-then-the-value-of-f-g-5-8-g-f-5-8-is
slug: let-x-denote-the-greatest-integer-x-if-f-x-x-and-g-x-x-then-the-value-of-f-g-5-8-g-f-5-8-is-49043
tags: ['Mathematics', 'Functions', 'BITSAT', 'BITSAT 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">-1</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">Let $[x]$ denote the greatest integer $\leq x$. If $f(x)=$ $[\mathrm{x}]$ and $g(x)=|x|,$ then the value of $\mathrm{f}\left(\mathrm{g}\left(\frac{8}{5}\right)\right)-\mathrm{g}\left(\mathrm{f}\left(-\frac{8}{5}\right)\right)$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">-2</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">-1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">$\begin{aligned}
<br/> <br/>&amp;\text { Given that, } f(x)=[x] \text { and } g(x)=|x|\\
<br/> <br/>&amp;\text { Now, } \mathrm{f}\left(\mathrm{g}\left(\frac{8}{5}\right)\right)=\mathrm{g}\left(\frac{8}{5}\right)=\left[\frac{8}{5}\right]=1
<br/> <br/>\end{aligned}$
<br/> <br/>and $\mathrm{g}\left(\mathrm{f}\left(-\frac{8}{5}\right)\right)=\mathrm{g}\left(\left[-\frac{8}{5}\right]\right)=\mathrm{g}(-2)=|-2|=2$
<br/> <br/>$\therefore \mathrm{f}\left(\mathrm{g}\left(\frac{8}{5}\right)\right)-\mathrm{g}\left(\mathrm{f}\left(-\frac{8}{5}\right)\right)=1-2=-1$</div>


title: let-x-y-3-cos-4-and-x-y-4-sin-2-then-the-greatest-of-x-y-is
slug: let-x-y-3-cos-4-and-x-y-4-sin-2-then-the-greatest-of-x-y-is-99457
tags: ['Mathematics', 'Application of Derivatives', 'BITSAT', 'BITSAT 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">Let $x+y=3-\cos 4 \theta$ and $x-y=4 \sin 2 \theta$ then the greatest of $x y$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3}{4}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2</span> </li> </ul>

answer:
<div class="solution">$x=\frac{3-\cos 4 \theta+4 \sin 2 \theta}{2}$
<br/> <br/>$=\frac{3-\left(1-\sin ^{2} 2 \theta\right)+4 \sin 2 \theta}{2}=(1+\sin 2 \theta)^{2}$
<br/> <br/>$y=\frac{3-\cos 4 \theta-4 \sin 2 \theta}{2}$
<br/> <br/>$=\frac{3-\left(1-\sin ^{2} 2 \theta\right)+4 \sin 2 \theta}{2}=(1-\sin 2 \theta)^{2}$
<br/> <br/>$\therefore x y=\left(1-\sin ^{2} 2 \theta\right)^{2}=\cos ^{4} 2 \theta \leq 1$</div>


title: liebigs-method-is-used-for-the-estimation-of
slug: liebigs-method-is-used-for-the-estimation-of-77245
question: <div class="question">Liebig's method is used for the estimation of</div>
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Nitrogen</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Sulphur</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Carbon and hydrogen</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Halogens</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Carbon and hydrogen</span> </div>


tags: ['Physics', 'Dual Nature of Matter', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch2_P2.db
title:
light-of-wavelength-180-nm-ejects-photoelectron-from-a-plate-of-a-metal-whose-work-function-is-2-ev-if-a-uniform-magnetic-field-of-5-1-0-5-t-is-applie

slug:
light-of-wavelength-180-nm-ejects-photoelectron-from-a-plate-of-a-metal-whose-work-function-is-2-ev-if-a-uniform-magnetic-field-of-5-1-0-5-t-is-applie-18872

question:
<div class="question">Light of wavelength $180 \mathrm{nm}$ ejects photoelectron from a plate of a metal whose work function is $2 \mathrm{eV}$. If a uniform magnetic field of $5 \times 10^{-5} \mathrm{~T}$ is applied parallel to plate, what would be theradius of the path followed by electrons ejected normally from the plate with maximum energy?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1.239 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0.149 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3.182 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2.33 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.149 \mathrm{~m}$</span> </div>

answer:
<div class="solution">If $\mathrm{v}_{\max }$ is the speed of the fastest electron emitted from the metal surface, then<br/>$$<br/>\begin{aligned}<br/>&amp; \frac{h c}{\lambda}=W_{0}+\frac{1}{2} m v_{\max }^{2} \frac{\left(6.63 \times 10^{-34}\right) \times\left(3 \times 10^{8}\right)}{\left(180 \times 10^{-9}\right)} \\<br/>&amp;=2 \times\left(1.6 \times 10^{-19}\right)+\frac{1}{2}\left(9.1 \times 10^{-31}\right) v_{\max }^{2} \\<br/>\therefore \quad &amp; v=1.31 \times 10^{6} \mathrm{~m} / \mathrm{s}<br/>\end{aligned}<br/>$$<br/>The radius of the electron is given by<br/>$$<br/>r=\frac{m v}{q B}=\frac{\left(9.1 \times 10^{-31}\right) \times\left(1.31 \times 10^{6}\right)}{\left(1.6 \times 10^{-19}\right) \times\left(5 \times 10^{-9}\right)}=0.149 \mathrm{~m}<br/>$$</div>


title: lim-n-a-n-b-n-a-n-b-n-where-a-b-1-is-equal-to
slug: lim-n-a-n-b-n-a-n-b-n-where-a-b-1-is-equal-to-15143
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">$\lim _{n \rightarrow \infty} \frac{a^{n}+b^{n}}{a^{n}-b^{n}},$ where $a&gt;b&gt;1,$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">-1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None</span> </li> </ul>

answer:
<div class="solution">limit $=\lim _{n \rightarrow \infty} \frac{1+\left(\frac{b}{a}\right)^{n}}{1-\left(\frac{b}{a}\right)^{n}}=1,$
<br/> <br/>because $0&lt;\frac{b}{a}&lt;1$ implies
<br/> <br/>$\left(\frac{b}{a}\right)^{n} \rightarrow 0$ as $n \rightarrow \infty$</div>


title: lim-n-sin-n-2-1-is-equal-to
slug: lim-n-sin-n-2-1-is-equal-to-82501
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P2.db
question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mi>sin</mi><mfenced close="]" open="["><mrow><mi>π</mi><msqrt><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></msqrt></mrow></mfenced></math> is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∞</mo></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">does not exist</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mi>sin</mi><mfenced close="}" open="{"><mrow><mi>n</mi><mi>π</mi><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><msup><mi>n</mi><mn>2</mn></msup></mfrac></mrow></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mi>sin</mi><mfenced close="}" open="{"><mrow><mi>n</mi><mi>π</mi><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><msup><mi>n</mi><mn>2</mn></msup></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mn>8</mn><msup><mi>n</mi><mn>4</mn></msup></mrow></mfrac><mo>+</mo><mo>…</mo></mrow></mfenced></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mi>sin</mi><mfenced close="}" open="{"><mrow><mi>n</mi><mi>π</mi><mo>+</mo><mfrac><mi>π</mi><mrow><mn>2</mn><mi>n</mi></mrow></mfrac><mo>-</mo><mfrac><mi>π</mi><mrow><mn>8</mn><msup><mi>n</mi><mn>3</mn></msup></mrow></mfrac><mo>+</mo><mo>…</mo></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><msup><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mi>n</mi></msup><mi>sin</mi><mi>π</mi><mfenced><mrow><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mn>8</mn><msup><mi>n</mi><mn>3</mn></msup></mrow></mfrac><mo>+</mo><mo>…</mo></mrow></mfenced><mo>=</mo><mn>0</mn></math></p></div>


title: lim-x-0-cosec-x-1-l-o-g-x-is-equal-to
slug: lim-x-0-cosec-x-1-l-o-g-x-is-equal-to-70633
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P2.db
question:
<div class="question">$\lim _{x \rightarrow 0}(\operatorname{cosec} x)^{1 / \log x}$ is equal to :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{e}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{e}$</span> </div>

answer:
<div class="solution">Let $y=\lim _{x \rightarrow 0}(\operatorname{cosec} x)^{1 / \log x}$
<br/> <br/>Taking $\log$ on both sides, we get
<br/> <br/>$\log y=\lim _{x \rightarrow 0} \frac{\log \operatorname{cosec} x}{\log x}\left[\frac{\infty}{\infty}\right.$ form $]$
<br/> <br/>$=\lim _{x \rightarrow 0} \frac{-\cot x}{1 / x} \quad$ (ByL' Hospital rule)
<br/> <br/>$=-\lim _{x \rightarrow 0} \frac{x}{\tan x} \quad\left(\because \cot x=\frac{1}{\tan x}\right)$
<br/> <br/>$\Rightarrow \log y=-1$
<br/> <br/>$\Rightarrow y=e^{-1}=\frac{1}{e}$
<br/> <br/>Hence, required limit $=\frac{1}{e}$</div>


title: lim-x-0-x-2-2-s-i-n-2-3-x-is-equal-to
slug: lim-x-0-x-2-2-s-i-n-2-3-x-is-equal-to-28269
question: <div class="question">$\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}$ is equal to</div>
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">18</span> </div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">12</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">18</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">6</span> </li> </ul>

answer:
<div class="solution">Consider $\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}$
<br/> <br/>$\begin{array}{l}
<br/> <br/>=2 \cdot \lim _{x \rightarrow 0}\left[\frac{\sin 3 x}{x}\right]^{2}=2 \cdot \lim _{x \rightarrow 0}\left[3 \frac{\sin 3 x}{3 x}\right]^{2} \\
<br/> <br/>=2.9 \lim _{x \rightarrow 0}\left(\frac{\sin 3 x}{3 x}\right)^{2}=18 \times 1=18
<br/> <br/>\end{array}$</div>


title: lim-x-0-x-s-i-n-2-x-x-s-i-n-x-is-equal-to
slug: lim-x-0-x-s-i-n-2-x-x-s-i-n-x-is-equal-to-71704
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">$\lim _{x \rightarrow 0} \sqrt{\frac{x-\sin x}{x+\sin ^{2} x}}$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">0</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\infty$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

answer:
<div class="solution">$\lim _{x \rightarrow 0} \sqrt{\frac{x-\sin x}{x+\sin ^{2} x}=\lim _{x \rightarrow 0} \sqrt{\frac{1-\frac{\sin x}{x}}{1+\frac{\sin ^{2} x}{x}}}}$
<br/> <br/>$=\lim _{x \rightarrow 0} \sqrt{\frac{1-\frac{\sin x}{x}}{1+\left(\frac{\sin x}{x}\right) \sin x}}=\sqrt{\frac{1-1}{1+1 \times 0}}=0$</div>


title: lim-x-0-x-s-i-n-x-is-equal-to-1
slug: lim-x-0-x-s-i-n-x-is-equal-to-1-89370
question: <div class="question">$\lim _{x \rightarrow 0} \frac{|\sin x|}{x}$ is equal to</div>
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">-1</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Does not exist</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Does not exist</span> </div>

answer:
<div class="solution">Let $l=\lim _{x \rightarrow 0} \frac{[\sin x]}{x} ; \mathrm{RHL}=\lim _{x \rightarrow 0^{+}} \frac{\sin x}{x}=1$<br/>$\mathrm{LHL}=\lim _{x \rightarrow 0^{-}}\left(\frac{-\sin x}{x}\right)=-\left(\lim _{x \rightarrow 0^{-}} \frac{\sin x}{x}\right)=-1$<br/>$\left[|x|=\begin{array}{c}x \text { if } x \geq 0 \\ -x \text { if } x \leq 0\end{array}\right]$<br/>As, LHL $\neq$ RHL Hence, limit $l$.does not exist.</div>


title: lim-x-2-1-t-a-n-2-x-2-x-3-1-t-a-n-2-x-1-s-i-n-x
slug: lim-x-2-1-t-a-n-2-x-2-x-3-1-t-a-n-2-x-1-s-i-n-x-76398
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P2.db
question:
<div class="question">$\lim _{x \rightarrow \pi / 2} \frac{\left(1-\tan \left(\frac{x}{2}\right)\right)(1-\sin x)}{\left(1+\tan \left(\frac{x}{2}\right)\right)(\pi-2 x)^{3}}=?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 / 8$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1 / 32$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\infty$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 / 32$</span> </div>

answer:
<div class="solution">Put $x=\frac{\pi}{2}-h$ as $x \rightarrow \frac{\pi}{2}, h \rightarrow 0$
<br/>$\therefore$ Given limit
<br/>$=\lim _{h \rightarrow 0} \frac{1-\tan \left(\frac{\pi}{4}-\frac{\mathrm{h}}{2}\right)}{1+\tan \left(\frac{\pi}{4}-\frac{\mathrm{h}}{2}\right)} \cdot \frac{(1-\cosh )}{(2 \mathrm{~h})^{3}}$
<br/>$=\lim _{\mathrm{h} \rightarrow 0} \tan \frac{\mathrm{h}}{2} \frac{2 \sin ^{2} \frac{\mathrm{h}}{2}}{8 \mathrm{~h}^{3}}$
<br/>$=\lim _{\mathrm{h} \rightarrow 0} \frac{1}{4} \cdot \frac{\tan \frac{\mathrm{h}}{2}}{\frac{\mathrm{h}}{2} \times 2}\left(\frac{\sin \frac{\mathrm{h}}{2}}{\frac{\mathrm{h}}{2}}\right)^{2} \times \frac{1}{4}$
<br/>$=\lim _{\mathrm{h} \rightarrow 0} \frac{1}{32} \cdot\left(\frac{\tan \frac{\mathrm{h}}{2}}{\frac{\mathrm{h}}{2} \times 2}\right)\left(\frac{\sin \frac{\mathrm{h}}{2}}{\frac{\mathrm{h}}{2}}\right)^{2}=\frac{1}{32}$</div>


title: lim-x-e-4-x-2-0-2-x-x-e-x-2-d-x-equals
slug: lim-x-e-4-x-2-0-2-x-x-e-x-2-d-x-equals-67985
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P2.db
question:
<div class="question">$$\lim _{x \rightarrow \infty} \frac{\int_{0}^{2 x} x e^{x^{2}} d x}{e^{4 x^{2}}} \text { equals }$$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\underline{0}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\infty$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Consider $\lim _{x \rightarrow \infty} \frac{\int_{0}^{2 x} x e^{x^{2}} d x}{e^{4 x^{2}}}$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>=\lim _{x \rightarrow \infty} \frac{2 \int_{0}^{2 x} x e^{x^{2}} d x}{2 e^{4 x^{2}}} \\
<br/> <br/>=\lim _{x \rightarrow \infty} \frac{2 \int_{0}^{2 x} e^{x^{2}} d\left(x^{2}\right)}{2 e^{4 x^{2}}} \\
<br/> <br/>=\lim _{x \rightarrow \infty} \frac{\left[e^{x^{2}}\right]_{0}^{2 x}}{e^{4 x^{2}}}=\lim _{x \rightarrow \infty} \frac{e^{4 x^{2}}-1}{2 e^{4 x^{2}}} \\
<br/> <br/>=\lim _{x \rightarrow \infty}\left(\frac{1}{2}-\frac{1}{2 e^{4 x^{2}}}\right)=\frac{1}{2}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


title: line-joining-the-points-0-3-and-5-2-is-a-tangent-to-the-curve-y-a-x-1-x-then
slug: line-joining-the-points-0-3-and-5-2-is-a-tangent-to-the-curve-y-a-x-1-x-then-80924
tags: ['Mathematics', 'Application of Derivatives', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P2.db
question:
<div class="question">Line joining the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo></math> is a tangent to the curve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mi>x</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>x</mi></mrow></mfrac></math>, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>±</mo><msqrt><mn>3</mn></msqrt></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>∈</mo><mi>ϕ</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>±</mo><msqrt><mn>3</mn></msqrt></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>±</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>∈</mo><mi>ϕ</mi></math></span> </div>

answer:
<div class="solution"><p>Equation of line joining the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>3</mn><mo>-</mo><mi>x</mi></math>.</p><p>If this line is tangent to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mi>x</mi></mrow><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac></math>, then</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>3</mn><mo>-</mo><mi>x</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>=</mo><mi>a</mi><mi>x</mi></math> should have equal roots. </p><p>Thus, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>-</mo><mn>2</mn><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> No value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>⇒</mo><mi>a</mi><mo>∈</mo><mi>ϕ</mi></math></p></div>


title: line-x-1-y-1-z-2-4-is-perpendicular-to-2-x-2-y-8-z-5-0-then-is
slug: line-x-1-y-1-z-2-4-is-perpendicular-to-2-x-2-y-8-z-5-0-then-is-15732
tags: ['Mathematics', 'Three Dimensional Geometry', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P2.db
question:
<div class="question">Line <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mi>λ</mi></mfrac><mo>=</mo><mi>y</mi><mo>-</mo><mn>1</mn><mo>=</mo><mfrac><mfenced><mrow><mi>z</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mrow><mo>-</mo><mn>4</mn></mrow></mfrac></math> is perpendicular to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>-</mo><mn>8</mn><mi>z</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>0</mn></math>, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math> is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> </div>

answer:
<div class="solution"><p>When line <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><msub><mi>x</mi><mn>1</mn></msub></mrow><msub><mi>a</mi><mn>1</mn></msub></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><msub><mi>y</mi><mn>1</mn></msub></mrow><msub><mi>b</mi><mn>1</mn></msub></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>-</mo><msub><mi>z</mi><mn>1</mn></msub></mrow><msub><mi>c</mi><mn>1</mn></msub></mfrac></math> is perpendicular to plane <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>+</mo><mi>c</mi><mi>z</mi><mo>+</mo><mi>d</mi><mo>=</mo><mn>0</mn></math>, then</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>a</mi><mn>1</mn></msub><mi>a</mi></mfrac><mo>=</mo><mfrac><msub><mi>b</mi><mn>1</mn></msub><mi>b</mi></mfrac><mo>=</mo><mfrac><msub><mi>c</mi><mn>1</mn></msub><mi>c</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mfrac><mi>λ</mi><mn>2</mn></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mo>-</mo><mn>4</mn></mrow><mrow><mo>-</mo><mn>8</mn></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>λ</mi><mo>=</mo><mn>1</mn></math></p><p>Hence, option (a) is correct.</p></div>


tags: ['Chemistry', 'Solutions', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch2_P2.db
title:
liquids-a-and-b-form-an-ideal-solution-in-the-entire-composition-range-at-350-k-the-vapor-pressures-of-pure-a-and-pure-b-are-7-1-0-3-pa-and-12-1-0-3-p

slug:
liquids-a-and-b-form-an-ideal-solution-in-the-entire-composition-range-at-350-k-the-vapor-pressures-of-pure-a-and-pure-b-are-7-1-0-3-pa-and-12-1-0-3-p-98004

question:
<div class="question">Liquids A and B form an ideal solution in the entire composition range. At $350 \mathrm{~K}$, the vapor pressures of pure A and pure B are $7 \times 10^{3} \mathrm{~Pa}$ and $12 \times 10^{3} \mathrm{~Pa}$, respectively. The composition of the vapour is in equilibrium with a solution containing 40 mole percent of $\mathrm{A}$ at this temperature is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$x_{\mathrm{A}}=0.37 ; x_{\mathrm{B}}=0.63$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$x_{\mathrm{A}}=0.28 ; x_{\mathrm{B}}=0.72$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$x_{\mathrm{A}}=0.4 ; x_{\mathrm{B}}=0.6$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$x_{\mathrm{A}}=0.76 ; x_{\mathrm{B}}=0.24$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x_{\mathrm{A}}=0.28 ; x_{\mathrm{B}}=0.72$</span> </div>

answer:
<div class="solution">$\mathrm{P}_{\mathrm{A}}^{\circ}=7 \times 10^{3}$
<br/> <br/>$\mathrm{P}_{\mathrm{B}}^{\circ}=12 \times 10^{3}$
<br/> <br/>$x_{\mathrm{A}}^{\prime}=0.4 ; x_{\mathrm{B}}^{\prime}=1-0.4$
<br/> <br/>$x_{\mathrm{B}}^{\prime}=0.6$
<br/> <br/>$\mathrm{P}_{\text {total }}=\mathrm{P}_{\mathrm{A}^{\circ}}^{x_{\mathrm{A}}^{\prime}}+\mathrm{P}_{\mathrm{B}}^{\circ} x_{\mathrm{B}}^{\prime}$
<br/> <br/>$=7 \times 10^{3} \times 0.4+12 \times 10^{3} \times 0.6$
<br/> <br/>$=(7 \times 0.4+12 \times 0.6) \times 10^{3}=10^{4}$
<br/> <br/>$x_{\mathrm{A}}=\frac{\mathrm{P}_{\mathrm{A}^{\circ}}^{x^{\prime}} \mathrm{A}}{\mathrm{P}_{\text {total }}}=\frac{7 \times 10^{3} \times 0.4}{10^{4}}$
<br/> <br/>$\therefore x_{\mathrm{A}}=0.28, x_{\mathrm{B}}=1-0.28=0.72$</div>


title: m-1-n-tan-1-2-m-m-4-m-2-2-is-equal-to
slug: m-1-n-tan-1-2-m-m-4-m-2-2-is-equal-to-61557
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch2_P2.db
question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mn>2</mn><mi>m</mi></mrow><mrow><msup><mi>m</mi><mn>4</mn></msup><mo>+</mo><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow></mfrac></mfenced></math> is equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac></mfenced></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>n</mi></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac></mfenced></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi></mrow></mfrac></mfenced></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac></mfenced></math></span> </div>

answer:
<div class="solution"><p>We have, <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mn>2</mn><mi>m</mi></mrow><mrow><msup><mi>m</mi><mn>4</mn></msup><mo>+</mo><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow></mfrac></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mfenced><mrow><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><msup><mi>m</mi><mn>2</mn></msup><mo>-</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>1</mn><mo>+</mo><mfenced><mrow><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msup><mi>m</mi><mn>2</mn></msup><mo>-</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><munderover><mo>∑</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfenced close="]" open="["><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>-</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><msup><mi>m</mi><mn>2</mn></msup><mo>-</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mn>3</mn><mo>-</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mn>1</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mn>7</mn><mo>-</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mn>3</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mn>13</mn><mo>)</mo><mo>-</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mn>7</mn></mrow></mfenced><mo>+</mo><mo>…</mo><mo>+</mo><mfenced close=""><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mfenced open=""><mrow><mo>-</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>-</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>-</mo><mn>1</mn></mrow><mrow><mn>1</mn><mo>+</mo><mfenced><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mfenced><mo>=</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi></mrow><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac></mfenced></math></p></div>


title: magnesium-burns-in-co-2-to-form
slug: magnesium-burns-in-co-2-to-form-94149
question: <div class="question">Magnesium burns in $\mathrm{CO}_2$ to form</div>
tags: ['Chemistry', 's Block Elements', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{MgO}+\mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{MgO}+\mathrm{CO}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{MgCO}_3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>MgO</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{MgO}+\mathrm{C}$</span> </div>

answer:
<div class="solution">$\mathrm{Mg}$ burns in $\mathrm{CO}_2$ to give $\mathrm{MgO}$ and $\mathrm{C}$.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P2.db
title:
magnetic-moment-of-bar-magnet-is-m-the-work-done-to-turn-the-magnet-by-9-0-of-magnet-in-direction-of-magnetic-field-b-will-be

slug:
magnetic-moment-of-bar-magnet-is-m-the-work-done-to-turn-the-magnet-by-9-0-of-magnet-in-direction-of-magnetic-field-b-will-be-15292

question:
<div class="question">Magnetic moment of bar magnet is $\mathrm{M}$. The work done to turn the magnet by $90^{\circ}$ of magnet in direction of magnetic field $\mathrm{B}$ will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">zero</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2} \mathrm{MB}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \mathrm{MB}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{MB}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{MB}$</span> </div>

answer:
<div class="solution">Work done, $\mathrm{W}=\mathrm{MB}(1-\cos \theta)$
<br/>$\theta=90^{\circ}$
<br/>$\mathrm{W}=\mathrm{MB}$</div>


title: maleic-acid-and-fumaric-acids-are-1
slug: maleic-acid-and-fumaric-acids-are-1-82487
question: <div class="question">Maleic acid and fumaric acids are</div>
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Chain isomers</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Functional isomers</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Tautomers</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Geometrical isomers</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Geometrical isomers</span> </div>

answer:
<div class="solution">Maleic acid and fumaric acids are geometrical isomers.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6g5mUYq1HbBCOFgQI_bTLZLV-ntesFRcTziwkZ3QS5E.original.fullsize.png"/></div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'JEE Main']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch2_P2.db
title:
match-list-i-reaction-with-list-ii-reagent-and-select-the-correct-answer-using-the-codes-given-below-the-lists-1

slug:
match-list-i-reaction-with-list-ii-reagent-and-select-the-correct-answer-using-the-codes-given-below-the-lists-1-47951

question:
<div class="question">Match List I (Reaction) with List II (Reagent) and select the correct answer using the codes given below the lists:<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/8hVpQ4ARAN3Q9tIOSzpXg0LxITwnkhyilk1Ki2kFkt0.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad \mathrm{I}-\mathrm{A}, \mathrm{II}-\mathrm{B}, \mathrm{III}-\mathrm{C}, \mathrm{IV}-\mathrm{B}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\quad \mathrm{I}-\mathrm{D}, \mathrm{II}-\mathrm{C}, \mathrm{III}-\mathrm{A}, \mathrm{IV}-\mathrm{B}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\quad \mathrm{I}-\mathrm{C}, \mathrm{II}-\mathrm{D}, \mathrm{III}-\mathrm{A}, \mathrm{IV}-\mathrm{B}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\quad \mathrm{I}-\mathrm{B}, \mathrm{II}-\mathrm{A}, \mathrm{III}-\mathrm{D}, \mathrm{IV}-\mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad \mathrm{I}-\mathrm{C}, \mathrm{II}-\mathrm{D}, \mathrm{III}-\mathrm{A}, \mathrm{IV}-\mathrm{B}$</span> </div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch2_P2.db
title:
match-list-i-reaction-with-list-ii-reagent-and-select-the-correct-answer-using-the-codes-given-below-the-lists

slug:
match-list-i-reaction-with-list-ii-reagent-and-select-the-correct-answer-using-the-codes-given-below-the-lists-17464

question:
<div class="question">Match List I (Reaction) with List II (Reagent) and select the correct answer using the codes given below the lists:<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/8hVpQ4ARAN3Q9tIOSzpXg0LxITwnkhyilk1Ki2kFkt0.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad \mathrm{I}-\mathrm{A}, \mathrm{II}-\mathrm{B}, \mathrm{III}-\mathrm{C}, \mathrm{IV}-\mathrm{B}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\quad \mathrm{I}-\mathrm{D}, \mathrm{II}-\mathrm{C}, \mathrm{III}-\mathrm{A}, \mathrm{IV}-\mathrm{B}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\quad \mathrm{I}-\mathrm{C}, \mathrm{II}-\mathrm{D}, \mathrm{III}-\mathrm{A}, \mathrm{IV}-\mathrm{B}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\quad \mathrm{I}-\mathrm{B}, \mathrm{II}-\mathrm{A}, \mathrm{III}-\mathrm{D}, \mathrm{IV}-\mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad \mathrm{I}-\mathrm{C}, \mathrm{II}-\mathrm{D}, \mathrm{III}-\mathrm{A}, \mathrm{IV}-\mathrm{B}$</span> </div>


tags: ['Mathematics', 'Functions', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch2_P2.db
title:
match-list-i-with-list-ii-and-select-the-correct-answer-using-the-code-given-below-the-lists-beginarrayll-textlist-i-textlist-ii-hline-texta-fxcos-x-t

slug:
match-list-i-with-list-ii-and-select-the-correct-answer-using-the-code-given-below-the-lists-beginarrayll-textlist-i-textlist-ii-hline-texta-fxcos-x-t-42648

question:
<div class="question">Match List I with List II and select the correct answer using the code given below the lists:
<br/>\(\begin{array}{l|l} \text{List I} &amp; \text{List II} \\ \hline \text{(A)} f(x)=\cos x &amp; \text{1. The graph cuts y-axis in infinite number of points} \\ \text{(B)} f(x)=\ln x &amp; \text{2. The graph cuts x-axis in two points} \\ \text{(C)} f(x)=x^2-5 x+43. &amp; \text{3. The graph cuts y-axis in only one point} \\ \text{(D)} f(x)=e^x &amp; \text{4. The graph cuts x-axis in only one point} \\  &amp; \text{5. The graph cuts x-axis in infinite number of points} \end{array}\)Codes:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">(A) - 1, (B) - 4, (C) - 5, (D) - 3</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">(A) - 1, (B) - 3, (C) - 5, (D) - 4</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">(A) - 5, (B) - 4, (C) - 2, (D) - 3</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">(A) - 5, (B) - 3, (C) - 2, (D) - 4</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">(A) - 5, (B) - 4, (C) - 2, (D) - 3</span> </div>

answer:
<div class="solution">(A) Graph of $f(x)=\cos x$ cuts $x$ -axis at infinite number of points. ( 5 of list II)
<br/> <br/>(B) Graph of $f(x)=\operatorname{In} x$ cuts $x$ -axis in only one point. (4 of list II)
<br/> <br/>(C) Graph of $f(x)=x^{2}-5 x+4$ cuts $x$ axis in two points ( 2 of list II)
<br/> <br/>(D) Graph of $\mathrm{f}(\mathrm{x})=\mathrm{e}^{\mathrm{x}}$ cuts $\mathrm{y}$ -axis in only one point. (3 of list II)</div>


tags: ['Chemistry', 'Polymers', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P2.db
title:
match-the-polymer-given-in-column-i-with-correct-monomer-of-column-ii-and-choose-the-correct-option-column-i-column-ii-a-neoprene-i-isoprene-b-natural

slug:
match-the-polymer-given-in-column-i-with-correct-monomer-of-column-ii-and-choose-the-correct-option-column-i-column-ii-a-neoprene-i-isoprene-b-natural-72194

question:
<div class="question"><p>Match the polymer given in column I with correct monomer of column II and choose the correct option.</p><table border="1" cellpadding="1" cellspacing="1" style="width: 500px;"> <tbody> <tr> <td style="text-align: center;"> </td> <td style="text-align: center;">Column I</td> <td style="text-align: center;"> </td> <td style="text-align: center;">Column II</td> </tr> <tr> <td style="text-align: center;">A.</td> <td>Neoprene</td> <td style="text-align: center;">I.</td> <td>Isoprene</td> </tr> <tr> <td style="text-align: center;">B.</td> <td>Natural rubber</td> <td style="text-align: center;">II.</td> <td>Tetrafluoro ethane</td> </tr> <tr> <td style="text-align: center;">C.</td> <td>Teflon</td> <td style="text-align: center;">III.</td> <td>Chloroprene</td> </tr> <tr> <td style="text-align: center;">D.</td> <td>Acrilan</td> <td style="text-align: center;">IV.</td> <td>Acryl nitrile</td> </tr> </tbody></table></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">A</mi></mtd><mtd><mi mathvariant="normal">B</mi></mtd><mtd><mi mathvariant="normal">C</mi></mtd><mtd><mi mathvariant="normal">D</mi></mtd></mtr><mtr><mtd><mi>IV</mi></mtd><mtd><mi>III</mi></mtd><mtd><mi>II</mi></mtd><mtd><mi mathvariant="normal">I</mi></mtd></mtr></mtable></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left left left left"><mtr><mtd><mi mathvariant="normal">A</mi></mtd><mtd><mi mathvariant="normal">B</mi></mtd><mtd><mi mathvariant="normal">C</mi></mtd><mtd><mi mathvariant="normal">D</mi></mtd></mtr><mtr><mtd><mi mathvariant="normal">I</mi></mtd><mtd><mi>II</mi></mtd><mtd><mi>III</mi></mtd><mtd><mi>IV</mi></mtd></mtr></mtable></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">A</mi></mtd><mtd><mi mathvariant="normal">B</mi></mtd><mtd><mi mathvariant="normal">C</mi></mtd><mtd><mi mathvariant="normal">D</mi></mtd></mtr><mtr><mtd><mi>III</mi></mtd><mtd><mi mathvariant="normal">I</mi></mtd><mtd><mi>II</mi></mtd><mtd><mi>IV</mi></mtd></mtr></mtable></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left left left left"><mtr><mtd><mi mathvariant="normal">A</mi></mtd><mtd><mi mathvariant="normal">B</mi></mtd><mtd><mi mathvariant="normal">C</mi></mtd><mtd><mi mathvariant="normal">D</mi></mtd></mtr><mtr><mtd><mi>II</mi></mtd><mtd><mi>IV</mi></mtd><mtd><mi mathvariant="normal">I</mi></mtd><mtd><mi>III</mi></mtd></mtr></mtable></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">A</mi></mtd><mtd><mi mathvariant="normal">B</mi></mtd><mtd><mi mathvariant="normal">C</mi></mtd><mtd><mi mathvariant="normal">D</mi></mtd></mtr><mtr><mtd><mi>III</mi></mtd><mtd><mi mathvariant="normal">I</mi></mtd><mtd><mi>II</mi></mtd><mtd><mi>IV</mi></mtd></mtr></mtable></math></span> </div>

answer:
<div class="solution"><p>Monomers basically create blocks for molecules, including proteins, starch and many other polymers. Four big monomers are found: amino acids, nucleotides, monosaccharides, and fatty acids. The main forms of macromolecules are those monomers: proteins, nucleic acids, carbohydrates, and lipids.<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/015f7191-e2a9-424a-a21d-fd08f73c0e95-6ad25077-1d9a-4f17-abbe-482d256b3f5d-9e325498-0795-41b0-acba-97fdccd22eef-image.png" style="width: 537px; height: 436px;"/></p></div>


title: match-the-species-in-column-i-with-their-types-in-column-ii-codes
slug: match-the-species-in-column-i-with-their-types-in-column-ii-codes-48041
tags: ['Chemistry', 'Coordination Compounds', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P2.db
question:
<div class="question">Match the species in Column I with their types in Column II.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/By8XOCIgUQhU_HxTxE-HHoSBVJoNHWc8SN-de7gMuX8.original.fullsize.png"/><br/> <br/>Codes</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"> <br/>$\mathrm{A} \rightarrow 4, \mathrm{~B} \rightarrow 3, \mathrm{C} \rightarrow 2, \mathrm{D} \rightarrow 1$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$\mathrm{A} \rightarrow 1, \mathrm{~B} \rightarrow 2, \mathrm{C} \rightarrow 3, \mathrm{D} \rightarrow 1$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$\mathrm{A} \rightarrow 2, \mathrm{~B} \rightarrow 3, \mathrm{C} \rightarrow 1, \mathrm{D} \rightarrow 4$
<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>$\mathrm{A} \rightarrow 3, \mathrm{~B} \rightarrow 1, \mathrm{C} \rightarrow 2, \mathrm{D} \rightarrow 4$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$\mathrm{A} \rightarrow 4, \mathrm{~B} \rightarrow 3, \mathrm{C} \rightarrow 2, \mathrm{D} \rightarrow 1$
<br/></span> </div>

answer:
<div class="solution">The correct match is
<br/>$\mathrm{A} \rightarrow(4) ; \mathrm{B} \rightarrow(3) ; \mathrm{C} \rightarrow(2) ; \mathrm{D} \rightarrow(1)$
<br/>A. DDT $\quad \rightarrow$ Pesticides
<br/>B. $\mathrm{NaClO}_3 \rightarrow$ Herbicides
<br/>C. $\mathrm{Cl}_2 \rightarrow$ Disinfectant
<br/>D. PAN $\quad \rightarrow$ Photochemical smog</div>


title: maximum-pk-b-value-is-of
slug: maximum-pk-b-value-is-of-41062
tags: ['Chemistry', 'Amines', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P2.db
question:
<div class="question">Maximum <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>pK</mi><mi mathvariant="normal">b</mi></msub></math> value is of </div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/892301c2-dcab-4ce6-9d04-fd5c95c1f201-image.png" style="width: 120px; height: 155px;"/></p></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mfenced><mrow><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CH</mi><mn>2</mn></msub></mrow></mfenced><mn>2</mn></msub><mi>NH</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced><mn>2</mn></msub><mi>NH</mi></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/106826dd-1642-402e-80ef-d0ccfd7f88e9-image.png" style="width: 200px; height: 59px;"/></p></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/106826dd-1642-402e-80ef-d0ccfd7f88e9-image.png" style="width: 200px; height: 59px;"/></p></span> </div>

answer:
<div class="solution"><p>Maximum <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>pK</mi><mi mathvariant="normal">b</mi></msub></math> (least basic) is (d) since, lone pair on<br/>N-atom is used to delocalise <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math> -electrons on two benzene<br/>rings.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/8d2d198b-a01d-4120-96c2-7c4b8d6b9d53-image.png" style="width: 260px; height: 107px;"/></p><p>Least basic has maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>pK</mi><mi mathvariant="normal">b</mi></msub></math>.</p><p>Since, in (d), lone pair of electrons over <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">N</mi></math>-atom are delocalised to two benzene rings, thus is least basic.</p></div>


tags: ['Mathematics', 'Statistics', 'BITSAT', 'BITSAT 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">79.48</span> </div>
source_db: MarksBatch2_P2.db
title:
mean-of-25-observations-was-found-to-be-784-but-later-on-it-was-found-that-96-was-misread-69-the-correct-mean-is

slug:
mean-of-25-observations-was-found-to-be-784-but-later-on-it-was-found-that-96-was-misread-69-the-correct-mean-is-73728

question:
<div class="question">Mean of 25 observations was found to be 78.4. But later on it was found that 96 was misread 69 . The correct mean is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">79.24</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">79.48</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">80.10</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

answer:
<div class="solution">Mean \(\bar{x}=\frac{\sum x}{n}\) or \(\Sigma x=n \bar{x}\)<br/>\(\Sigma \mathrm{x}=25 \times 78.4=1960\)<br/>But this \(\Sigma \mathrm{x}\) is incorrect as 96 was misread as 69 .<br/>\(\begin{aligned}<br/>&amp; \therefore \text { correct } \Sigma \mathrm{x}=1960+(96-69)=1987 \\<br/>&amp; \therefore \text { correct mean }=\frac{1987}{25}=79.48<br/>\end{aligned}\)</div>


title: melamine-plastic-crockery-is-a-copolymer-of
slug: melamine-plastic-crockery-is-a-copolymer-of-53935
question: <div class="question">Melamine plastic crockery is a copolymer of</div>
tags: ['Chemistry', 'Polymers', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{HCHO}$ and melamine</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{HCHO}$ and ethylene</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">melamine and ethylene</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{HCHO}$ and melamine</span> </div>

answer:
<div class="solution">Melamine plastic crockery is a copolymer of $\mathrm{HCHO}$ and Melamine.</div>


tags: ['Chemistry', 'Surface Chemistry', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch2_P2.db
title:
methylene-blue-from-its-aqueous-solution-is-adsorbed-on-activated-charcoal-at-2-5-c-for-this-process-which-ofthe-following-statement-is-correct

slug:
methylene-blue-from-its-aqueous-solution-is-adsorbed-on-activated-charcoal-at-2-5-c-for-this-process-which-ofthe-following-statement-is-correct-37867

question:
<div class="question">Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at $25^{\circ} \mathrm{C}$. For this process, which ofthe following statement is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The adsorption requires activation at $25^{\circ} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">The adsorption is accompanied by a decrease in enthalpy</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The adsorption increases with increase of temperature</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The adsorption is irreversible</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The adsorption is accompanied by a decrease in enthalpy</span> </div>

answer:
<div class="solution">The adsorption of methylene blue on activated charcoal is an example of physiosorption which is exothermic, multilayer and does not have energy barrier.</div>


title: mi-of-a-circular-loop-of-radius-r-about-the-axis-in-figure-is
slug: mi-of-a-circular-loop-of-radius-r-about-the-axis-in-figure-is-13814
tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2020']
answer: <div class="solution">Use theorem of parallel axes.</div>
source_db: MarksBatch2_P2.db
question:
<div class="question">M.I of a circular loop of radius $\mathrm{R}$ about the axis in figure is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/wKFguHAttmGuk0D7ytnbZUzSjJtulAv3RLaJS6JFPS8.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{MR}^{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$(3 / 4) \mathrm{MR}^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{MR}^{2} / 2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \mathrm{MR}^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(3 / 4) \mathrm{MR}^{2}$</span> </div>


title: minamata-disease-is-due-to-pollution-of-3
slug: minamata-disease-is-due-to-pollution-of-3-34688
question: <div class="question">Minamata disease is due to pollution of</div>
tags: ['Chemistry', 'Environmental Chemistry', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">Minamata is caused by Hg poisoning.</div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">aresenic into the atmosphere</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">organic waste into drinking water</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">oil spill in water</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">industrial waste mercury into fishing water</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">industrial waste mercury into fishing water</span> </div>


tags: ['Mathematics', 'Linear Programming', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P2.db
title:
minimise-z-j-1-n-i-1-m-c-ij-x-ij-subject-to-i-1-m-x-ij-b-j-j-1-2-n-j-1-n-x-ij-b-j-i-1-2-m-is-a-l-pp-with-number-of-constr

slug:
minimise-z-j-1-n-i-1-m-c-ij-x-ij-subject-to-i-1-m-x-ij-b-j-j-1-2-n-j-1-n-x-ij-b-j-i-1-2-m-is-a-l-pp-with-number-of-constr-68299

question:
<div class="question">Minimise $Z=\sum_{j=1}^{n} \sum_{i=1}^{m} c_{i j} x_{i j}$
<br/> <br/>Subject to $\sum_{i=1}^{m} x_{i j}=b_{j}, j=1,2, \ldots, n$
<br/> <br/>$\sum_{j=1}^{n} x_{i j}=b_{j}, i=1,2, \ldots, m$ is a $L P P$ with number of constr</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$m-n$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$m$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{m}+\mathrm{n}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mathrm{m}}{\mathrm{n}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{m}+\mathrm{n}$</span> </div>

answer:
<div class="solution">Constraints will be
<br/> <br/>$$
<br/> <br/>\mathrm{x}_{11}+\mathrm{x}_{21}+\ldots .+\mathrm{x}_{\mathrm{ml}}=\mathrm{b}_{1}
<br/> <br/>$$
<br/> <br/>$\mathrm{x}_{12}+\mathrm{x}_{22}+\ldots \ldots \mathrm{x}_{\mathrm{m} 2}=\mathrm{b}_{2}$
<br/> <br/>$\mathrm{x}_{\ln }+\mathrm{x}_{2 \mathrm{n}}+\ldots .+\mathrm{x}_{\mathrm{mn}}=\mathrm{b}_{\mathrm{n}}$
<br/> <br/>$\mathrm{x}_{11}+\mathrm{x}_{12}+\ldots+\mathrm{x}_{1 \mathrm{n}}=\mathrm{b}_{1}$
<br/> <br/>$\mathrm{x}_{21}+\mathrm{x}_{22}+\ldots+\mathrm{x}_{2 \mathrm{n}}=\mathrm{b}_{2}$
<br/> <br/>$\mathrm{x}_{\mathrm{ml}}+\mathrm{x}_{\mathrm{m} 2}+\ldots+\mathrm{x}_{\mathrm{mn}}=\mathrm{b}_{\mathrm{n}}$
<br/> <br/>So, total number of constraints $=\mathrm{m}+\mathrm{n}$</div>


title: minimum-value-of-z-3-x-5-y-subject-to-constraints-x-y-2-x-3-y-3-x-y-0
slug: minimum-value-of-z-3-x-5-y-subject-to-constraints-x-y-2-x-3-y-3-x-y-0-72077
tags: ['Mathematics', 'Linear Programming', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value"><br/>7</span> </div>
answer: <div class="solution">$\mathrm{Z}$ is 7 minimum at $\left(\frac{3}{2}, \frac{1}{2}\right)$</div>
source_db: MarksBatch2_P2.db
question:
<div class="question">Minimum value of $Z=3 x+5 y$ subject to constraints $x+y \geq 2, x+3 y \geq 3, x, y \geq 0$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>6</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>7</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>8</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>9</span> </li> </ul>


tags: ['Physics', 'Dual Nature of Matter', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch2_P2.db
title:
monochromatic-light-of-wavelength-667-nm-is-produced-by-a-helium-neon-laser-the-power-emitted-is-9-mw-the-number-of-photons-arriving-per-sec-on-the-av

slug:
monochromatic-light-of-wavelength-667-nm-is-produced-by-a-helium-neon-laser-the-power-emitted-is-9-mw-the-number-of-photons-arriving-per-sec-on-the-av-86334

question:
<div class="question">Monochromatic light of wavelength $667 \mathrm{~nm}$ is produced by a helium neon laser. The power emitted is $9 \mathrm{~mW}$. The number of photons arriving per sec on the average at a target irradiated by this beam is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$3 \times 10^{16}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$9 \times 10^{15}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3 \times 10^{19}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$9 \times 10^{17}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 \times 10^{16}$</span> </div>

answer:
<div class="solution">$\lambda=667 \times 10^{-9} m, \mathrm{P}=9 \times 10^{-3} \mathrm{~W}$
<br/> <br/>$\mathrm{P}=\frac{\text { Nhc }}{\lambda}, \mathrm{N}=$ No. of photons emitted/sec.
<br/> <br/>$\mathrm{N}=\frac{9 \times 10^{-3} \times 667 \times 10^{-9}}{6.6 \times 10^{-34} \times 3 \times 10^{8}}=3 \times 10^{16} / \mathrm{sec}$</div>


tags: ['Physics', 'Atomic Physics', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P2.db
title:
monochromatic-radiation-of-wavelength-is-incident-on-a-hydrogen-sample-in-ground-state-hydrogen-atom-absorbs-a-fraction-of-light-and-subsequently-emit

slug:
monochromatic-radiation-of-wavelength-is-incident-on-a-hydrogen-sample-in-ground-state-hydrogen-atom-absorbs-a-fraction-of-light-and-subsequently-emit-93296

question:
<div class="question">Monochromatic radiation of wavelength <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math> is incident on a hydrogen sample in ground state. Hydrogen atom absorbs a fraction of light and subsequently emits radiations of six different wavelengths. The wavelength <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math> is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>97</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>nm</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>121</mn><mo>.</mo><mn>6</mn><mo> </mo><mi>nm</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>110</mn><mo>.</mo><mn>3</mn><mo> </mo><mi>nm</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>.</mo><mn>2</mn><mo> </mo><mi>nm</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>97</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>nm</mi></math></span> </div>

answer:
<div class="solution"><p>As <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">H</mi></math>-atom emits <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> spectral lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mn>2</mn></mfrac><mo>=</mo><mn>6</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>n</mi><mo>=</mo><mn>4</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi><mi>E</mi><mo>=</mo><msub><mi>E</mi><mn>4</mn></msub><mo>-</mo><msub><mi>E</mi><mn>1</mn></msub><mo>=</mo><mn>13</mn><mo>.</mo><mn>6</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>85</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>12</mn><mo>.</mo><mn>75</mn><mo> </mo><mi>eV</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mrow><mi>h</mi><mi>c</mi></mrow><mrow><mo>∆</mo><mi>E</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1242</mn><mo> </mo><mi>nm</mi></mrow><mrow><mn>12</mn><mo>.</mo><mn>75</mn></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi>λ</mi><mo>=</mo><mn>97</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>nm</mi></math></p></div>


tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P2.db
title:
n-2-and-o-2-are-converted-into-mono-anions-n-2-and-o-2-respectively-which-of-the-following-statements-is-wrong

slug:
n-2-and-o-2-are-converted-into-mono-anions-n-2-and-o-2-respectively-which-of-the-following-statements-is-wrong-86664

question:
<div class="question">$\mathrm{N}_{2}$ and $\mathrm{O}_{2}$ are converted into mono anions, $\mathrm{N}_{2}^{-}$ and $\mathrm{O}_{2}^{-}$ respectively. Which of the following statements is wrong ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\operatorname{In} \mathrm{N}_{2}$, the $\mathrm{N}-\mathrm{N}$ bond weakens</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">In $\mathrm{O}_{2}$, the $\mathrm{O}-\mathrm{O}$ bond order increases</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">In $\mathrm{O}_{2},$ bond length decreases</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{N}_{2}^{-}$ becomes diamagnetic</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">In $\mathrm{O}_{2}$, the $\mathrm{O}-\mathrm{O}$ bond order increases</span> </div>

answer:
<div class="solution">We know that in $\mathrm{O}_{2}$ bond, the order is 2 and in $\mathrm{O}_{2}^{-}$ bond, the order is 1.5 . Therefore the wrong statements is (b).</div>


title: n-cf-2-cf-2-nh-4-2-s-2-o-8-benzoyl-peroxide-or-x-here-x-is
slug: n-cf-2-cf-2-nh-4-2-s-2-o-8-benzoyl-peroxide-or-x-here-x-is-88494
tags: ['Chemistry', 'Polymers', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch2_P2.db
question:
<div class="question">$\mathrm{n}\left(\mathrm{CF}_{2}=\mathrm{CF}_{2}\right) \frac{\text { Benzoyl peroxide or }}{\left(\mathrm{NH}_{4}\right)_{2} \mathrm{~S}_{2} \mathrm{O}_{8}} \mathrm{X}$
<br/> <br/>Here, $\mathrm{X}$ is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">RMMA</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{PVC}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{PAN}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of these</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/tJbjMAdgpu5xHO4EsfGoQEZJz8gTqCHhVejZjLG433c.original.fullsize.png"/><br/> <br/> <br/>Here $X$ is polytetrafluoroethylene. So, none of these i.e., option (d) is correct choice.</div>


title: name-of-following-reaction-is-1
slug: name-of-following-reaction-is-1-61907
tags: ['Chemistry', 'Hydrocarbons', 'JEE Main']
answer: <div class="solution">The given reaction is Diel's Alder reaction.</div>
source_db: MarksBatch2_P2.db
question:
<div class="question">Name of following reaction is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/SpGFiyfeRQpa1MpXLTY_FRHMY6b4ok0zqJIAqM0p5AQ.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Claisen Condensation</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Diel's Alder reaction</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Dieckmann cyclisation</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Michael addition reaction</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Diel's Alder reaction</span> </div>


title: negation-of-paris-in-france-and-london-is-in-england-is
slug: negation-of-paris-in-france-and-london-is-in-england-is-75748
question: <div class="question">Negation of "Paris in France and London is in England" is</div>
tags: ['Mathematics', 'Mathematical Reasoning', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Paris is in England and London is in France</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Paris is not in France or London is not in England</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Paris is in England or London is in France</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Paris is not in France or London is not in England</span> </div>

answer:
<div class="solution">Let \(p\) : Paris is in France, \(q\) : London is in England<br/>\(\therefore \quad\) we have \(p \wedge q\)<br/>Its negation is \(\sim(p \wedge q)=\sim p \vee \sim q\)<br/>i.e., Paris is not in France or London is not in England.</div>


title: negation-of-the-boolean-expression-p-q-p-is-1
slug: negation-of-the-boolean-expression-p-q-p-is-1-97499
tags: ['Mathematics', 'Mathematical Reasoning', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">Negation of the Boolean expression $\mathrm{p} \Leftrightarrow(\mathrm{q} \Rightarrow \mathrm{p})$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(\sim p) \wedge q$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(\mathrm{p}) \wedge(\sim \mathrm{q})$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(\sim \mathrm{p}) \vee(\sim \mathrm{q})$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$(\sim p) \wedge(\sim q)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(\sim p) \wedge(\sim q)$</span> </div>

answer:
<div class="solution">Given expression is $p \Leftrightarrow(q \Rightarrow p)$<br/>$\sim(\mathrm{p} \leftrightarrow(\mathrm{q} \rightarrow \mathrm{p}))$<br/>$\sim(\mathrm{p} \leftrightarrow \mathrm{q})=(\mathrm{p} \wedge \sim \mathrm{q}) \vee(\mathrm{q} \wedge \sim \mathrm{p})$<br/>$\sim(\mathrm{p} \leftrightarrow(\mathrm{q} \rightarrow \mathrm{p}))$ $=(\mathrm{p} \wedge \sim(\mathrm{q} \rightarrow \mathrm{p})) \vee((\mathrm{q} \rightarrow \mathrm{p}) \wedge \sim \mathrm{p})$<br/>$(\mathrm{p} \wedge \sim(\mathrm{q} \rightarrow \mathrm{p}))=\mathrm{p} \wedge(\mathrm{q} \wedge \sim \mathrm{p})$ $=(p \wedge \sim p) \wedge q=c$<br/>$(q \rightarrow p) \wedge \sim p=(\sim q \vee p) \wedge \sim p$ $=\sim p \wedge(\sim q \vee p)$<br/>$=(\sim \mathrm{p} \wedge \sim \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{p})=\sim \mathrm{p} \wedge \sim \mathrm{q}$<br/>$\sim(p \leftrightarrow(\dot{q} \rightarrow p))=c \vee(\sim p \wedge \sim q)=\sim p \wedge \sim q$</div>


title: neoprene-is-a
slug: neoprene-is-a-97134
question: <div class="question">Neoprene is a</div>
tags: ['Chemistry', 'Polymers', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">monomer of rubber</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">synthetic rubber</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">a natural rubber</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">vulcanised rubber</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">synthetic rubber</span> </div>

answer:
<div class="solution">Neoprene is a synthetic rubber. It is a polymer of chloroprene (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>-chlorobuta,<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>3</mn></math> diene).</div>


title: ninhydrin-gives-yellow-colour-in-paper-chromatography-with-which-amino-acid
slug: ninhydrin-gives-yellow-colour-in-paper-chromatography-with-which-amino-acid-90013
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P2.db
question:
<div class="question">Ninhydrin gives yellow colour in paper chromatography with which amino acid?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>Tryptophan
<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"> <br/>Proline
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>Alanine
<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>Tyrosine</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>Proline
<br/></span> </div>

answer:
<div class="solution">The amino acid which gives yellow colour with ninhydrin in paper chromatography is proline.
<br/>Ninhydrin + Proline $\longrightarrow$ Yellow-orange product</div>


title: nitrogen-is-obtained-by-the-thermal-decomposition-of
slug: nitrogen-is-obtained-by-the-thermal-decomposition-of-34065
question: <div class="question">Nitrogen is obtained by the thermal decomposition of:</div>
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{NH}_{4} \mathrm{NO}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{NH}_{4} \mathrm{NO}_{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{AgNO}_{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{NH}_{4} \mathrm{NO}_{2}$</span> </div>

answer:
<div class="solution">$\mathrm{NH}_{4} \mathrm{NO}_{2} \stackrel{\Delta}{\rightarrow} \mathrm{N}_{2}+2 \mathrm{H}_{2} \mathrm{O}$</div>


tags: ['Mathematics', 'Parabola', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P2.db
title:
normals-drawn-to-y-2-4-a-x-at-the-points-where-it-is-intersected-by-the-line-y-m-x-c-intersected-at-p-coordinates-of-foot-of-the-another-normal-drawn-

slug:
normals-drawn-to-y-2-4-a-x-at-the-points-where-it-is-intersected-by-the-line-y-m-x-c-intersected-at-p-coordinates-of-foot-of-the-another-normal-drawn-86625

question:
<div class="question">Normals drawn to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn><mi>a</mi><mi>x</mi></math> at the points where it is intersected by the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>c</mi></math> intersected at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math>. Coordinates of foot of the another normal drawn to the parabola from the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mi>a</mi><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>2</mn><mi>a</mi></mrow><mi>m</mi></mfrac></mrow></mfenced></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>9</mn><mi>m</mi></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>6</mn><mi>a</mi></mrow><mi>m</mi></mfrac></mrow></mfenced></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>a</mi><msup><mi>m</mi><mn>2</mn></msup><mo>,</mo><mo>-</mo><mn>2</mn><mi>a</mi><mi>m</mi></mrow></mfenced></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>4</mn><mi>a</mi></mrow><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>4</mn><mi>a</mi></mrow><mi>m</mi></mfrac></mrow></mfenced></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>4</mn><mi>a</mi></mrow><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>4</mn><mi>a</mi></mrow><mi>m</mi></mfrac></mrow></mfenced></math></span> </div>

answer:
<div class="solution"><p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>c</mi></math>, intersect <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn><mi>a</mi><mi>x</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mfenced><mrow><mi>a</mi><msubsup><mi>t</mi><mn>1</mn><mn>2</mn></msubsup><mo>,</mo><mn>2</mn><mi>a</mi><msub><mi>t</mi><mn>1</mn></msub></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mfenced><mrow><mi>a</mi><msubsup><mi>t</mi><mn>2</mn><mn>2</mn></msubsup><mo>,</mo><mn>2</mn><mi>a</mi><msub><mi>t</mi><mn>2</mn></msub></mrow></mfenced></math>.</p><p>Then, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mrow><msub><mi>t</mi><mn>1</mn></msub><mo>+</mo><msub><mi>t</mi><mn>2</mn></msub></mrow></mfrac><mo>=</mo><mi>m</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi>t</mi><mn>1</mn></msub><mo>+</mo><msub><mi>t</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>2</mn><mi>m</mi></mfrac></math></p><p>Let the foot of another normal be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mfenced><mrow><mi>a</mi><msubsup><mi>t</mi><mn>3</mn><mn>2</mn></msubsup><mo>,</mo><mn>2</mn><mi>a</mi><msub><mi>t</mi><mn>3</mn></msub></mrow></mfenced></math></p><p>Then, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>1</mn></msub><mo>+</mo><msub><mi>t</mi><mn>2</mn></msub><mo>+</mo><msub><mi>t</mi><mn>3</mn></msub><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>3</mn></msub><mo>=</mo><mfenced><mrow><msub><mi>t</mi><mn>1</mn></msub><mo>+</mo><msub><mi>t</mi><mn>2</mn></msub></mrow></mfenced><mo>=</mo><mo>-</mo><mfrac><mn>2</mn><mi>m</mi></mfrac></math></p><p>Thus, other foot is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>4</mn><mi>a</mi></mrow><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>,</mo><mfrac><mrow><mo>-</mo><mn>4</mn><mi>a</mi></mrow><mi>m</mi></mfrac></mrow></mfenced></math></p><p>Hence, option (d) is correct.</p></div>


title: nuclear-energy-is-released-in-fission-since-binding-energy-per-nucleon-is
slug: nuclear-energy-is-released-in-fission-since-binding-energy-per-nucleon-is-15376
tags: ['Physics', 'Nuclear Physics', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch2_P2.db
question:
<div class="question">Nuclear energy is released in fission since binding energy per nucleon is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">sometimes larger and sometimes smaller</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">larger for fission fragments than for parent nucleus</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">same for fission fragments and nucleus</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">smaller for fission fragments than for parent nucleus</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">larger for fission fragments than for parent nucleus</span> </div>

answer:
<div class="solution">Nuclear energy is relased in fission because $\mathrm{BE} /$ nucleon is larger for fission fragments than for parent nucleus.</div>


title: nucleophilic-addition-reaction-will-be-most-favoured-in
slug: nucleophilic-addition-reaction-will-be-most-favoured-in-86397
question: <div class="question">Nucleophilic addition reaction will be most favoured in</div>
tags: ['Chemistry', 'Aldehydes and Ketones', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{O}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CHO}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/f7G9zN15UtWp76yPv3ADyg08mr5Nei9lHPHhr7FoSz8.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{CH}_{3} \mathrm{CHO}$</span> </div>

answer:
<div class="solution">Aldehydes are more reactive than ketones due to $+\mathrm{I}$ effect of $-\mathrm{CH}_{3}$ group. There are two $-\mathrm{CH}_{3}$ group in acetone which reduces +ve charge density on carbon atom of carbonyl group. More hindered carbonyl group becomes less reactive. So in the given case $\mathrm{CH}_{3} \mathrm{CHO}$ is the right choice.</div>


title: number-of-atoms-of-he-in-100-amu-of-heatomic-wt-of-he-is-4-are
slug: number-of-atoms-of-he-in-100-amu-of-heatomic-wt-of-he-is-4-are-66896
question: <div class="question">Number of atoms of He in 100 amu of He(atomic wt. of He is 4) are:</div>
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2012']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">25</span> </div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">25</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">100</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">50</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$100 \times 6 \times 10^{-23}$</span> </li> </ul>

answer:
<div class="solution">$\begin{array}{l}
<br/>100 \text { amu of He }=\frac{100}{4} \text { atoms of He } \\
<br/>=25 \text { atoms. }
<br/>\end{array}$
<br/>$[1$ a.m.u. $=$ mass of one proton (approx.)]</div>


tags: ['Mathematics', 'Functions', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch2_P2.db
title:
number-of-solution-of-the-equation-cos-x-2-x-are-where-x-x-are-modulus-and-greatest-integer-function-respectively

slug:
number-of-solution-of-the-equation-cos-x-2-x-are-where-x-x-are-modulus-and-greatest-integer-function-respectively-59644

question:
<div class="question">Number of solution of the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>cos</mi><mi>x</mi><mo>|</mo><mo>=</mo><mn>2</mn><mo>[</mo><mi>x</mi><mo>]</mo></math> are (where <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>x</mi><mo>|</mo><mo>,</mo><mo>[</mo><mi>x</mi><mo>]</mo></math> are modulus and greatest integer function respectively).</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">infinitely many</span> </li> </ul>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>cos</mi><mi>x</mi><mo>|</mo><mo>=</mo><mn>2</mn><mo>[</mo><mi>x</mi><mo>]</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mo>|</mo><mi>cos</mi><mi>x</mi><mo>|</mo><mo>≤</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mn>0</mn><mo>≤</mo><mn>2</mn><mo>[</mo><mi>x</mi><mo>]</mo><mo>≤</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mo>[</mo><mi>x</mi><mo>]</mo><mo>≤</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mi>x</mi></mfenced><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>x</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></p><p>But <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>cos</mi><mi>x</mi><mo>|</mo><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>x</mi><mo>=</mo><mi>n</mi><mi>π</mi><mo>+</mo><mfrac><mi>π</mi><mn>2</mn></mfrac></math> for any value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>∈</mo><mi>Z</mi></math></p><p>Hence, the equation has no solution.</p></div>


title: number-of-words-from-the-letters-of-the-words-bharat-in-which-b-and-h-will-never-come-together-is
tags: ['Mathematics', 'Permutation Combination', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">240</span> </div>
source_db: MarksBatch2_P2.db
slug:
number-of-words-from-the-letters-of-the-words-bharat-in-which-b-and-h-will-never-come-together-is-41586

question:
<div class="question">Number of words from the letters of the words BHARAT in which $B$ and $\mathrm{H}$ will never come together is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">210</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">240</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">422</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">400</span> </li> </ul>

answer:
<div class="solution">There are 6 letters in the word BHARAT, 2 of them are identical. Hence total number of words $=6 ! / 2 !=360$<br/>Number of words in which $B$ and $\mathrm{H}$ come together<br/>$=\frac{5 ! 2 !}{2 !}=120$<br/>final ans $=360-120=240$</div>


title: nylon-66-is-obtained-from
slug: nylon-66-is-obtained-from-84816
question: <div class="question">Nylon- 6,6 is obtained from</div>
tags: ['Chemistry', 'Polymers', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"> <br/>adipic acid and hexamethylene diamine
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>tetrafluoroethylene
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>vinyl cyanide
<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>vinyl benzene</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>adipic acid and hexamethylene diamine
<br/></span> </div>

answer:
<div class="solution">The monomer units of nylon- 6,6 are hexamethylene diamine and adipic acid.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ezA-3QhZokOV8tao3TdTmiIdoE7wig3EVFBGxbthEE8.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Straight Lines', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P2.db
title:
o-p-q-r-is-a-square-and-m-n-are-the-middle-points-of-the-sides-p-q-and-q-r-respectively-then-the-ratio-of-the-areas-of-the-square-and-o-m-n-is

slug:
o-p-q-r-is-a-square-and-m-n-are-the-middle-points-of-the-sides-p-q-and-q-r-respectively-then-the-ratio-of-the-areas-of-the-square-and-o-m-n-is-49544

question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>P</mi><mi>Q</mi><mi>R</mi></math> is a square and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>,</mo><mo> </mo><mi>N</mi></math> are the middle points of the sides <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>Q</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>R</mi></math> respectively, then the ratio of the areas of the square and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi><mi>O</mi><mi>M</mi><mi>N</mi></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>1</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>:</mo><mn>1</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>:</mo><mn>3</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>3</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>:</mo><mn>3</mn></math></span> </div>

answer:
<div class="solution"><p>Taking the coordinates of vertices <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mi>O</mi><mo>,</mo><mo> </mo><mi>P</mi><mo>,</mo><mo> </mo><mi>Q</mi><mo>,</mo><mo> </mo><mi>R</mi></math> as <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mo> </mo><mo>(</mo><mi>a</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mo> </mo><mo>(</mo><mi>a</mi><mo>,</mo><mi>a</mi><mo>)</mo><mo>,</mo><mo> </mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>a</mi><mo>)</mo></math>, respectively.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> The coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>a</mi><mo>,</mo><mfrac><mi>a</mi><mn>2</mn></mfrac></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>,</mo><mi>a</mi></mrow></mfenced></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/f8cac160-83ae-4bf5-a06a-619f8a01946e-d49.png" style="width: 333px; height: 170px;"/></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi><mi>O</mi><mi>M</mi><mi>N</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced close="|" open="|"><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mi>a</mi></mtd><mtd><mi>a</mi><mo>/</mo><mn>2</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>/</mo><mn>2</mn></mtd><mtd><mi>a</mi></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>=</mo><mfrac><mrow><mn>3</mn><msup><mi>a</mi><mn>2</mn></msup></mrow><mn>8</mn></mfrac></math></p><p>and area of the square <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> The required ratio is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>:</mo><mn>3</mn></math>.</p><p>Hence, option (c) is correct.</p></div>


title: observe-the-given-boundary-surface-diagrams-of-two-orbitals-i-and-ii-and-choose-the-correct-option
tags: ['Chemistry', 'Structure of Atom', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P2.db
slug:
observe-the-given-boundary-surface-diagrams-of-two-orbitals-i-and-ii-and-choose-the-correct-option-67215

question:
<div class="question">Observe the given boundary surface diagrams of two orbitals I and II and choose the correct option.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/GYKz3EmQr_n_fr0MOL35Bk2XhGlRzEASRkVOxdpcEBs.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{I}-d_{x^2-y^2}, \mathrm{II}-d_{y z}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{I}-d_{y z}, \mathrm{II}-d_{x^2-y^2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{I}-d_{x z}, \mathrm{II}-d_{z^2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{I}-d_{x y}, \mathrm{II}-d_{x z}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{I}-d_{y z}, \mathrm{II}-d_{x^2-y^2}$</span> </div>

answer:
<div class="solution">In boundary surface diagram (1) the four lobes lie between $y$ and $z$-axis $\left(d_{y z}\right)$ whereas, in boundary surface diagram (2) the four lobes lie on the $x$ and $y$-axis $\left(d_{x^2-y^2}\right)$.</div>


title: of-and-f-2-can-be-compared-in-terms-of
slug: of-and-f-2-can-be-compared-in-terms-of-67466
question: <div class="question">$\mathrm{OF}$ and $\mathrm{F}_2$ can be compared in terms of</div>
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$\mathrm{OF}$ is paramagnetic while $\mathrm{F}_2$ is diamagnetic
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>OF is more stable towards dissociation into atoms
<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"> <br/>Both (a) and (b) are correct
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>None of the above is correct</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>Both (a) and (b) are correct
<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/BlF17NzSVsXnf9GsAVD-1smgvmLZQdQph_p7vuw3vZg.original.fullsize.png"/><br/> <br/>This is one unpaired electron in $(\mathrm{O}-\mathrm{F})$, hence paramagnetic, thus (a) is correct.
<br/>As bond order of $\mathrm{O}-\mathrm{F}&gt;\mathrm{F}-\mathrm{F}$ thus, bond energy of $\mathrm{O}-\mathrm{F}&gt;\mathrm{F}-\mathrm{F}$.
<br/>Hence, (a) and (b) both are correct.</div>


tags: ['Physics', 'Units and Dimensions', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P2.db
title:
on-a-temperature-scale-x-the-boiling-point-of-water-is-6-5-x-and-the-freezing-point-is-1-5-x-assume-that-the-x-scale-is-linear-the-equivalent-temperat

slug:
on-a-temperature-scale-x-the-boiling-point-of-water-is-6-5-x-and-the-freezing-point-is-1-5-x-assume-that-the-x-scale-is-linear-the-equivalent-temperat-86376

question:
<div class="question">On a temperature scale ' $X$ '. The boiling point of water is $65^{\circ} \mathrm{X}$ and the freezing point is $-15^{\circ} \mathrm{X}$. Assume that the $\mathrm{X}$ scale is linear. The equivalent temperature corresponding to $-95^{\circ} \mathrm{X}$ on the Farenheit scale would be:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-63^{\circ} \mathrm{F}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$-112^{\circ} \mathrm{F}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-48^{\circ} \mathrm{F}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$-148^{\circ} \mathrm{F}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-148^{\circ} \mathrm{F}$</span> </div>

answer:
<div class="solution">Boiling point of water, $=$ UFP $65^{\circ}$<br/>Freezing point of water, $=\mathrm{LFP}-15^{\circ}$<br/>$\frac{\mathrm{X}-\mathrm{LFP}}{\mathrm{UFP}-\mathrm{LFP}}=\frac{\mathrm{T}_{\mathrm{F}}-32}{212-32}$<br/>$\Rightarrow \frac{-95-(-15)}{65-(-15)}=\frac{\mathrm{T}_{\mathrm{F}}-32}{180}$<br/>$\Rightarrow \frac{-80}{80}=\frac{T_F-32}{180} \Rightarrow T_F=-180+32$<br/>$\Rightarrow \mathrm{T}_{\mathrm{F}}=-148^{\circ} \mathrm{F}$</div>


title: on-electrolysis-of-water-a-total-of-1-mole-of-gases-is-evolved-the-amount-of-water-decomposed-is
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P2.db
slug:
on-electrolysis-of-water-a-total-of-1-mole-of-gases-is-evolved-the-amount-of-water-decomposed-is-61010

question:
<div class="question">On electrolysis of water, a total of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>mole</mi></math> of gases is evolved. The amount of water decomposed is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>mol</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>mol</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo> </mo><mi>mol</mi></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><mo> </mo><mi>mol</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><mo> </mo><mi>mol</mi></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo></math> Only one mole of total gases are evolved and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math> decomposes as</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi><mover><mo>→</mo><mi>decomposition</mi></mover><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub></math></p><p>i.e. total moles <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math> moles by one mole of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math></p><p>Now,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math> moles of gases are evolved by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo> </mo><mi>mole</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mn>1</mn><mo> </mo><mi>mole</mi></math> of gases are evolved by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></p><p>Hence, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>mole</mi></math> of total gases are evolved by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><mo> </mo><mi>mole</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math>.</p></div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch2_P2.db
title:
on-reaction-with-sodium-1-mol-of-a-compound-x-gives-1-mol-of-h-2-which-one-of-the-following-compounds-might-be-x

slug:
on-reaction-with-sodium-1-mol-of-a-compound-x-gives-1-mol-of-h-2-which-one-of-the-following-compounds-might-be-x-61933

question:
<div class="question">On reaction with sodium, 1 mol of a compound $\mathrm{X}$ gives $1 \mathrm{~mol}$ of $\mathrm{H}_{2} .$ Which one of the following compounds might be $X ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}=\mathrm{CH}_{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{COOCH}_{2} \mathrm{CH}_{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_{2}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{CH}_{2}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$</span> </div>

answer:
<div class="solution">Since 1 mole of compound Xreacts with Na to evolve 1 mole of $\mathrm{H}_{2}$ gas, therefore the compound should have 2 active hydrogen atoms per mole which is possible only in option $d$.
<br/> <br/>$\begin{array}{l}
<br/> <br/>\mathrm{CH}_{2} \mathrm{OHCH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}+2 \mathrm{Na} \\
<br/> <br/>\longrightarrow \mathrm{NaOCH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{ONa}+2 \mathrm{H}
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Mechanical Properties of Solids', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
one-end-of-a-long-metallic-wire-of-length-l-tied-to-the-ceiling-the-other-end-is-tied-with-a-massless-spring-of-spring-constant-k-amass-hangs-freely-f-1

slug:
one-end-of-a-long-metallic-wire-of-length-l-tied-to-the-ceiling-the-other-end-is-tied-with-a-massless-spring-of-spring-constant-k-amass-hangs-freely-f-1-13229

question:
<div class="question">One end of a long metallic wire of length $\mathrm{L}$ tied to the ceiling. The other end is tied with a massless spring of spring constant $\mathrm{K}$. Amass hangs freely from the free end of the spring. The area of cross section and the young's modulus of the wire are A and Y respectively. If the mass slightly pulled down and released, it will oscillate with a time period T equal to:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \pi \sqrt{(\mathrm{m} / \mathrm{K})}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$2 \pi \sqrt{\mathrm{m}(\mathrm{YA}+\mathrm{KL}) /(\mathrm{YAK})}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \pi \sqrt{(\mathrm{m} \mathrm{YA} / \mathrm{KL})}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \pi \sqrt{(\mathrm{mL} / \mathrm{YA})}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \pi \sqrt{\mathrm{m}(\mathrm{YA}+\mathrm{KL}) /(\mathrm{YAK})}$</span> </div>

answer:
<div class="solution">Step 1: Calculation of spring constant of wire
<br/>Young's modulus of wire, \(\mathrm{Y}=\frac{\Delta \mathrm{F} / \mathrm{A}}{\Delta \mathrm{L} / \mathrm{L}}=\frac{\Delta \mathrm{F}}{\Delta \mathrm{L}} \times \frac{\mathrm{L}}{\mathrm{A}}\)
<br/>Due to elasticity of the wire, it behaves as equivalent spring \(\left(\mathrm{K}_{\text {spring }}=\mathrm{F} / \Delta \mathrm{x}\right)\).
<br/>Hence, Spring constant for Wire, \(\mathrm{K}_{\mathrm{w}}=\frac{\Delta \mathrm{F}}{\Delta \mathrm{L}}=\mathrm{Y} \frac{\mathrm{A}}{\mathrm{L}}\)
<br/>Step 2: Calculation of Equivalent spring constant Let a force \(\mathrm{F}\) be applied to the end of the spring. The wire will extend.
<br/>Total extension \(\Delta \mathrm{S}=\mathrm{x}_{\mathrm{wire}}+\mathrm{x}_{\text {spring }}=\frac{\mathrm{F}_{\mathrm{w}}}{\mathrm{K}_{\mathrm{w}}}+\frac{\mathrm{F}_{\mathrm{S}}}{\mathrm{K}}\)
<br/>But \(\mathrm{F}_{\mathrm{S}}=\mathrm{F}_{\mathrm{w}} \quad\) (By Newton's, third Law, Both will apply equal and opposite forces at their joint A )
<br/>\(\therefore \Delta \mathrm{S}=\mathrm{F}_{\mathrm{w}}\left(\frac{1}{\mathrm{~K}_{\mathrm{w}}}+\frac{1}{\mathrm{~K}}\right)\)
<br/>So, Equivalent spring constant \(\left(\mathrm{K}_{\text {eq }}\right)\) is given by:
<br/>\(\mathrm{K}_{\mathrm{eq}}=\frac{\mathrm{F}_{\mathrm{eq}}}{\mathrm{x}_{\mathrm{eq}}}=\frac{\mathrm{F}_{\mathrm{w}}}{\Delta \mathrm{S}}=\frac{1}{\frac{1}{\mathrm{~K}_{\mathrm{w}}}+\frac{1}{\mathrm{~K}}}\)
<br/>\(\mathrm{K}_{\mathrm{eq}}=\frac{(\mathrm{K})\left(\mathrm{K}_{\mathrm{w}}\right)}{\mathrm{K}_{\mathrm{w}}+\mathrm{K}}=\frac{\mathrm{KY} \frac{\mathrm{A}}{\mathrm{L}}}{\mathrm{Y} \frac{\mathrm{A}}{\mathrm{L}}+\mathrm{K}}=\frac{\mathrm{KYA}}{\mathrm{YA}+\mathrm{KL}}\)
<br/>Step 3: Calculation of Time period
<br/>Angular frequency \(\omega\) for spring block system is given by:
<br/>\(\omega=\sqrt{\frac{\mathrm{K}_{\text {eq }}}{\mathrm{m}}}=\sqrt{\frac{\mathrm{KYA}}{\mathrm{m}(\mathrm{YA}+\mathrm{KL})}}\)
<br/>\(\therefore\) Time period, \(\mathrm{T}=\frac{2 \pi}{\omega}=2 \pi \sqrt{\frac{(\mathrm{YA}+\mathrm{KL}) \mathrm{m}}{\mathrm{KYA}}}\)
<br/>Hence, Option B is correct
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/hwt6276qhuuqoipq82.png"/></div>


tags: ['Physics', 'Mechanical Properties of Solids', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P2.db
title:
one-end-of-a-long-metallic-wire-of-length-l-tied-to-the-ceiling-the-other-end-is-tied-with-a-massless-spring-of-spring-constant-k-amass-hangs-freely-f

slug:
one-end-of-a-long-metallic-wire-of-length-l-tied-to-the-ceiling-the-other-end-is-tied-with-a-massless-spring-of-spring-constant-k-amass-hangs-freely-f-73704

question:
<div class="question">One end of a long metallic wire of length $\mathrm{L}$ tied to the ceiling. The other end is tied with a massless spring of spring constant $\mathrm{K}$. Amass hangs freely from the free end of the spring. The area of cross section and the young's modulus of the wire are A and Y respectively. If the mass slightly pulled down and released, it will oscillate with a time period T equal to:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \pi \sqrt{(\mathrm{m} / \mathrm{K})}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$2 \pi \sqrt{\mathrm{m}(\mathrm{YA}+\mathrm{KL}) /(\mathrm{YAK})}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \pi \sqrt{(\mathrm{m} \mathrm{YA} / \mathrm{KL})}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \pi \sqrt{(\mathrm{mL} / \mathrm{YA})}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \pi \sqrt{\mathrm{m}(\mathrm{YA}+\mathrm{KL}) /(\mathrm{YAK})}$</span> </div>

answer:
<div class="solution">Step 1: Calculation of spring constant of wire
<br/>Young's modulus of wire, \(\mathrm{Y}=\frac{\Delta \mathrm{F} / \mathrm{A}}{\Delta \mathrm{L} / \mathrm{L}}=\frac{\Delta \mathrm{F}}{\Delta \mathrm{L}} \times \frac{\mathrm{L}}{\mathrm{A}}\)
<br/>Due to elasticity of the wire, it behaves as equivalent spring \(\left(\mathrm{K}_{\text {spring }}=\mathrm{F} / \Delta \mathrm{x}\right)\).
<br/>Hence, Spring constant for Wire, \(\mathrm{K}_{\mathrm{w}}=\frac{\Delta \mathrm{F}}{\Delta \mathrm{L}}=\mathrm{Y} \frac{\mathrm{A}}{\mathrm{L}}\)
<br/>Step 2: Calculation of Equivalent spring constant Let a force \(\mathrm{F}\) be applied to the end of the spring. The wire will extend.
<br/>Total extension \(\Delta \mathrm{S}=\mathrm{x}_{\mathrm{wire}}+\mathrm{x}_{\text {spring }}=\frac{\mathrm{F}_{\mathrm{w}}}{\mathrm{K}_{\mathrm{w}}}+\frac{\mathrm{F}_{\mathrm{S}}}{\mathrm{K}}\)
<br/>But \(\mathrm{F}_{\mathrm{S}}=\mathrm{F}_{\mathrm{w}} \quad\) (By Newton's, third Law, Both will apply equal and opposite forces at their joint A )
<br/>\(\therefore \Delta \mathrm{S}=\mathrm{F}_{\mathrm{w}}\left(\frac{1}{\mathrm{~K}_{\mathrm{w}}}+\frac{1}{\mathrm{~K}}\right)\)
<br/>So, Equivalent spring constant \(\left(\mathrm{K}_{\text {eq }}\right)\) is given by:
<br/>\(\mathrm{K}_{\mathrm{eq}}=\frac{\mathrm{F}_{\mathrm{eq}}}{\mathrm{x}_{\mathrm{eq}}}=\frac{\mathrm{F}_{\mathrm{w}}}{\Delta \mathrm{S}}=\frac{1}{\frac{1}{\mathrm{~K}_{\mathrm{w}}}+\frac{1}{\mathrm{~K}}}\)
<br/>\(\mathrm{K}_{\mathrm{eq}}=\frac{(\mathrm{K})\left(\mathrm{K}_{\mathrm{w}}\right)}{\mathrm{K}_{\mathrm{w}}+\mathrm{K}}=\frac{\mathrm{KY} \frac{\mathrm{A}}{\mathrm{L}}}{\mathrm{Y} \frac{\mathrm{A}}{\mathrm{L}}+\mathrm{K}}=\frac{\mathrm{KYA}}{\mathrm{YA}+\mathrm{KL}}\)
<br/>Step 3: Calculation of Time period
<br/>Angular frequency \(\omega\) for spring block system is given by:
<br/>\(\omega=\sqrt{\frac{\mathrm{K}_{\text {eq }}}{\mathrm{m}}}=\sqrt{\frac{\mathrm{KYA}}{\mathrm{m}(\mathrm{YA}+\mathrm{KL})}}\)
<br/>\(\therefore\) Time period, \(\mathrm{T}=\frac{2 \pi}{\omega}=2 \pi \sqrt{\frac{(\mathrm{YA}+\mathrm{KL}) \mathrm{m}}{\mathrm{KYA}}}\)
<br/>Hence, Option B is correct
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/hwt6276qhuuqoipq82.png"/></div>


tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch2_P2.db
title:
one-kilogram-of-ice-at-0-c-is-mixed-with-one-kilogram-of-water-at-8-0-c-the-final-temperature-of-the-mixture-is-take-specific-heat-of-water-4200-kj-kg

slug:
one-kilogram-of-ice-at-0-c-is-mixed-with-one-kilogram-of-water-at-8-0-c-the-final-temperature-of-the-mixture-is-take-specific-heat-of-water-4200-kj-kg-41648

question:
<div class="question">One kilogram of ice at $0^{\circ} \mathrm{C}$ is mixed with one kilogram of water at $80^{\circ} \mathrm{C}$. The final temperature of the mixture is (Take specific heat of water $=4200 \mathrm{~kJ} / \mathrm{kg}-{ }^{\circ} \mathrm{C},$ Latent heat of ice $\left.=336 \mathrm{~kJ} / \mathrm{kg}\right)$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0^{\rho} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$40^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$50^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$60^{\circ} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0^{\rho} \mathrm{C}$</span> </div>


tags: ['Physics', 'Kinetic Theory of Gases', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P2.db
title:
one-mole-of-an-ideal-diatomic-gas-undergoes-a-process-as-shown-in-the-figure-the-molar-specific-heat-of-the-gas-in-the-process-is

slug:
one-mole-of-an-ideal-diatomic-gas-undergoes-a-process-as-shown-in-the-figure-the-molar-specific-heat-of-the-gas-in-the-process-is-25351

question:
<div class="question">One mole of an ideal diatomic gas undergoes a process as shown in the figure. The molar specific heat of the gas in the process is
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/wZYV1jP2W2EUUOAi4XFZ99EiTwe_EEulWyjSo5CNNEA.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"> <br/>$3 R / 2$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/> $R / 2$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$5 R / 2$
<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>$7 R / 2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$3 R / 2$
<br/></span> </div>

answer:
<div class="solution">In the curve, $V \propto \frac{1}{T}$
<br/>$$
<br/>\begin{aligned}
<br/>&amp; \Rightarrow V=m \frac{1}{T} \text { where, } m=\text { slope of curve. } \\
<br/>&amp; \Rightarrow V T=\text { constant } \\
<br/>&amp; \therefore \quad T d V+V d T=0 \\
<br/>&amp; \Rightarrow \quad d V=-\frac{V}{T} d T \\
<br/>&amp; \text { As, } Q=\Delta U+W \\
<br/>&amp; C d T=C_V d T+p d V \\
<br/>&amp; C d T=C_V d T-\frac{p}{T} V d T \\
<br/>&amp; \Rightarrow \quad C=C_V-\frac{p V}{T} \\
<br/>&amp; =C_V-R \quad\left(\because \frac{p V}{T}=R\right) \\
<br/>&amp;
<br/>\end{aligned}
<br/>$$
<br/>For diatomic gas, $C_V=\frac{5}{2} R$
<br/>$$
<br/>\therefore \quad C=C_V-R=\frac{5}{2} R-R=\frac{3 R}{2}
<br/>$$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
answer: <div class="solution">For isothermal process, $\Delta \mathrm{E}=0$</div>
source_db: MarksBatch2_P2.db
title:
one-mole-of-an-ideal-gas-at-300-k-is-expanded-isothermally-from-an-initial-volume-of-1-litre-to-10-litres-the-e-for-this-process-is-r-2-cal-mol-1-k-1

slug:
one-mole-of-an-ideal-gas-at-300-k-is-expanded-isothermally-from-an-initial-volume-of-1-litre-to-10-litres-the-e-for-this-process-is-r-2-cal-mol-1-k-1-21233

question:
<div class="question">One mole of an ideal gas at $300 \mathrm{~K}$ is expanded isothermally from an initial volume of 1 litre to 10 litres. The $\Delta \mathrm{E}$ for this process is $\left(\mathrm{R}=2\right.$ cal $\left.\mathrm{mol}^{-1} \mathrm{~K}^{-1}\right)$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$163.7 \mathrm{cal}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1381.1 \mathrm{cal}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">9 lit atom</span> </li> </ul>


tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P2.db
title:
one-mole-of-o-2-gas-having-a-volume-equal-to-224-litres-at-0-c-and-1-atmospheric-pressure-in-compressed-isothermally-so-that-its-volume-reduces-to-112

slug:
one-mole-of-o-2-gas-having-a-volume-equal-to-224-litres-at-0-c-and-1-atmospheric-pressure-in-compressed-isothermally-so-that-its-volume-reduces-to-112-20315

question:
<div class="question">One mole of $\mathrm{O}_{2}$ gas having a volume equal to 22.4 Litres at $0^{\circ} \mathrm{C}$ and 1 atmospheric pressure in compressed isothermally so that its volume reduces to 11.2 litres. The work done in this process is-</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1672.5 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1728 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-1728 \mathrm{~J}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$-1572.5 \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-1572.5 \mathrm{~J}$</span> </div>

answer:
<div class="solution">Work done in adiabatic process, \(\mathrm{W}=\mu \mathrm{RT} \log _{\mathrm{e}}\left(\frac{\mathrm{V}_{\mathrm{f}}}{\mathrm{V}_{\mathrm{i}}}\right)\)
<br/> <br/>\(\mathrm{W}=1 \times 8.314 \times 273 \times \log _{\mathrm{e}}\left(\frac{11.2}{22.4}\right)\)
<br/> <br/>\(\mathrm{W}=8.314 \times 273 \times \log _{\mathrm{e}}\left(\frac{1}{2}\right)\)
<br/> <br/>\(\mathrm{W}=8.314 \times 273 \times\left[\log _{\mathrm{e}}(1)-\log _{\mathrm{e}}(2)\right]\)
<br/> <br/>\(\mathrm{W}=8.314 \times 273 \times(0-0.69)\)
<br/> <br/>\(\mathrm{W}=-1566.1 \mathrm{~J}\)</div>


tags: ['Chemistry', 'States of Matter', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P2.db
title:
one-moles-each-of-four-ideal-gases-are-kept-as-follows-i-5-l-of-gas-a-at-2-atm-pressure-ii-2-5-l-of-gas-b-at-2-atm-pressure-iii-1-25-l-of-gas-c-at-2-a

slug:
one-moles-each-of-four-ideal-gases-are-kept-as-follows-i-5-l-of-gas-a-at-2-atm-pressure-ii-2-5-l-of-gas-b-at-2-atm-pressure-iii-1-25-l-of-gas-c-at-2-a-78834

question:
<div class="question"><p>One moles each of four ideal gases are kept as follows. </p><p>I. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi mathvariant="normal">L</mi></math> of gas <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">A</mi><mo>)</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>atm</mi></math> pressure</p><p>II. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">L</mi></math> of gas <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">B</mi><mo>)</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>atm</mi></math> pressure</p><p>III. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">L</mi></math> of gas <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">C</mi><mo>)</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>atm</mi></math> pressure</p><p>IV. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">L</mi></math> of gas <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">D</mi><mo>)</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>atm</mi></math> pressure</p><p>Which of the above gases is kept at highest temperature.</p></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Gas <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">A</mi><mo>)</mo></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Gas <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">B</mi><mo>)</mo></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Gas <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">C</mi><mo>)</mo></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Gas <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">D</mi><mo>)</mo></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Gas <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">A</mi><mo>)</mo></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo></math> For ideals gas</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pV</mi><mo>=</mo><mi>nRT</mi></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi><mo>=</mo><mfrac><mi>pV</mi><mi>nR</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mi mathvariant="normal">n</mi><mo>=</mo><mn>1</mn><mo>=</mo></math> constant</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">R</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>083</mn><mo>=</mo></math> constant</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi mathvariant="normal">T</mi><mo>∝</mo><mi>PV</mi></math></p><p>Thus, </p><p>The gas that shows highest product of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>×</mo><mi mathvariant="normal">V</mi></math>, has highest temperature.</p><p>for<br/>(A) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>×</mo><mi mathvariant="normal">V</mi><mo>=</mo><mn>2</mn><mo>×</mo><mn>5</mn><mo>=</mo><mn>10</mn><mo> </mo><mi>atm</mi><mo> </mo><mi mathvariant="normal">L</mi></math></p><p>(B) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>×</mo><mi mathvariant="normal">V</mi><mo>=</mo><mn>2</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>=</mo><mn>5</mn><mo> </mo><mi>atmL</mi></math></p><p>(C) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>×</mo><mi mathvariant="normal">V</mi><mo>=</mo><mn>2</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>25</mn><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>atmL</mi><mo> </mo></math></p><p>(D) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>×</mo><mi mathvariant="normal">V</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>=</mo><mn>6</mn><mo>.</mo><mn>25</mn><mo> </mo><mi>atm</mi><mo> </mo><mi mathvariant="normal">L</mi></math></p><p>Hence gas <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">A</mi><mo>)</mo></math> show highest temperature.</p></div>


tags: ['Physics', 'Atomic Physics', 'BITSAT', 'BITSAT 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P2.db
title:
one-of-the-lines-in-the-emission-spectrum-of-li-2-has-the-same-wavelength-as-that-of-the-2-nd-line-of-balmer-series-in-hydrogen-spectrum-the-electroni

slug:
one-of-the-lines-in-the-emission-spectrum-of-li-2-has-the-same-wavelength-as-that-of-the-2-nd-line-of-balmer-series-in-hydrogen-spectrum-the-electroni-55443

question:
<div class="question">One of the lines in the emission spectrum of $\mathrm{Li}^{2+}$ has the same wavelength as that of the $2^{\text {nd }}$ line of Balmer series in hydrogen spectrum. The electronic transition corresponding to this line is $\mathrm{n}=12 \rightarrow \mathrm{n}=\mathrm{x} .$ Find the value of $\mathrm{x}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">8</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">6</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">7</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5</span> </li> </ul>

answer:
<div class="solution">For $2^{\text {nd line of Balmer series in hydrogen }}$ spectrum
<br/> <br/>$$
<br/> <br/>\frac{1}{\lambda}=\mathrm{R}(1)\left(\frac{1}{2^{2}}-\frac{1}{4^{2}}\right)=\frac{3}{16} \mathrm{R}
<br/> <br/>$$
<br/> <br/>$$
<br/> <br/>\text { For } \mathrm{Li}^{2+}\left[\frac{1}{\lambda}=\mathrm{R} \times 9\left(\frac{1}{\mathrm{x}^{2}}-\frac{1}{12^{2}}\right)=\frac{3 \mathrm{R}}{16}\right]
<br/> <br/>$$
<br/> <br/>which is satisfied by $n=12 \rightarrow n=6$</div>


title: ordinary-glass-is
slug: ordinary-glass-is-82759
question: <div class="question">Ordinary glass is:</div>
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Sodium silicate</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Calcium silicate</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Sodium and calcium silicate</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Mixed salt of $\mathrm{Na}$ and $\mathrm{Ca}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Sodium silicate</span> </div>

answer:
<div class="solution">Normal glass is calcium alkali silicate glass made by fusing the alkali metal carbonate, $\mathrm{CaCO}_{3}$ and $\mathrm{SiO}_{2}$</div>


title: ortho-and-para-form-of-hydrogen-have
slug: ortho-and-para-form-of-hydrogen-have-45775
question: <div class="question">ortho and para form of hydrogen have</div>
tags: ['Chemistry', 'Hydrogen', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>different physical and chemical properties
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/> identical physical properties but different chemical properties
<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"> <br/>identical chemical properties but different physical properties
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>identical chemical and physical properties</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>identical chemical properties but different physical properties
<br/></span> </div>

answer:
<div class="solution">Ortho and para hydrogen similar to each other in their chemical properties but they have different physical properties like boiling point, thermal conductivity, due to their difference in overall spins.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zOcmN1xViz_LzG6vg-f0HQRokroV91AmS1RAeR-HOeQ.original.fullsize.png"/><br/></div>


title: p-and-q-are-isomers-identify-q-1
slug: p-and-q-are-isomers-identify-q-1-99360
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main']
source_db: MarksBatch2_P2.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ukT0-8k5YGVPdc5dtHWqvLHcUzt_9MNsq0wF7JbCRwc.original.fullsize.png"/><br/> <br/> <br/>$\mathrm{P}$ and $\mathrm{Q}$ are isomers. Identify $\mathrm{Q}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/WG09pZIzE1hvT6QMihQLFaKrjIqG2z-ALR2ww8tDtv4.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Uvp851OTA2rlBRQwN95J1rV7_9Rz4v3y1al_9xdntIA.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/VaJvsWmItnUxXeriuM8P88c-rBQmDj9QbZT7evkkFes.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/sFMyFWMT5FYHKCMnGEFFVMkNxq5SXAoyI83eBGqB7b0.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/sFMyFWMT5FYHKCMnGEFFVMkNxq5SXAoyI83eBGqB7b0.original.fullsize.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/KfvoNyI_4P91c7Twts30tze904xZ5Qs5LE5lRvwQ9EY.original.fullsize.png"/></div>


tags: ['Chemistry', 'Chemical Equilibrium', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch2_P2.db
title:
pcl-5-is-dissociating-50-at-25-0-c-at-a-total-pressure-of-p-atm-if-equilibrium-constant-is-k-p-then-which-of-the-following-relation-is-numerically-cor

slug:
pcl-5-is-dissociating-50-at-25-0-c-at-a-total-pressure-of-p-atm-if-equilibrium-constant-is-k-p-then-which-of-the-following-relation-is-numerically-cor-92764

question:
<div class="question">$\mathrm{PCl}_{5}$ is dissociating $50 \%$ at $250^{\circ} \mathrm{C}$ at a total pressure of $\mathrm{P}$ atm. If equilibrium constant is $\mathrm{K}_{p}$, then which of the following relation is numerically correct -</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{K}_{p}=3 \mathrm{P}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{P}=3 \mathrm{~K}_{p}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{P}=\frac{2 K_{\mathrm{P}}}{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{~K}_{p}=\frac{2 \mathrm{P}}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{P}=3 \mathrm{~K}_{p}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/FF1dZ-oqNNSNDytMXuA1tI9bURJwNDZa08chwNZLWZg.original.fullsize.png"/><br/> <br/> <br/>$\mathrm{K}_{\mathrm{p}}=\frac{\frac{\mathrm{P}}{3} \times \frac{\mathrm{P}}{3}}{\frac{\mathrm{P}}{3}}=\frac{\mathrm{P}}{3}$</div>


title: period-of-fracsin-thetasin-2-thetacos-thetacos-2-theta-is
slug: period-of-fracsin-thetasin-2-thetacos-thetacos-2-theta-is-11010
tags: ['Mathematics', 'Trigonometric Equations', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch2_P2.db
question:
<div class="question">Period of \(\frac{\sin \theta+\sin 2 \theta}{\cos \theta+\cos 2 \theta}\) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(2 \pi\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\pi\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(\frac{2 \pi}{3}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\frac{\pi}{3}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\frac{2 \pi}{3}\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \frac{\sin \theta+\sin 2 \theta}{\cos \theta+\cos 2 \theta}=\frac{2 \sin \left(\frac{3 \theta}{2}\right) \cos \left(\frac{\theta}{2}\right)}{2 \cos \left(\frac{3 \theta}{2}\right) \cos \left(\frac{\theta}{2}\right)}=\tan \left(\frac{3 \theta}{2}\right) \\<br/>&amp; \text {Hence period }=\frac{2 \pi}{3}<br/>\end{aligned}\)</div>


title: ph-of-a-saturated-solution-of-ba-oh-2-is-12-the-value-of-its-k-sp-is
slug: ph-of-a-saturated-solution-of-ba-oh-2-is-12-the-value-of-its-k-sp-is-29906
tags: ['Chemistry', 'Ionic Equilibrium', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P2.db
question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pH</mi></math> of a saturated solution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ba</mi><msub><mfenced><mi>OH</mi></mfenced><mn>2</mn></msub></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> . The value of its <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mi>sp</mi></msub></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">M</mi><mn>3</mn></msup></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">M</mi><mn>3</mn></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">M</mi><mn>3</mn></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mi mathvariant="normal">M</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">M</mi><mn>3</mn></msup></math></span> </div>

answer:
<div class="solution"><p>Given that,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pH</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ba</mi><msub><mfenced><mi>OH</mi></mfenced><mn>2</mn></msub><mo>=</mo><mn>12</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mi>pH</mi><mo>+</mo><mi>pOH</mi><mo>=</mo><mn>14</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>pOH</mi><mo>=</mo><mn>14</mn><mo>-</mo><mi>pH</mi><mo>=</mo><mn>14</mn><mo>-</mo><mn>12</mn><mo>=</mo><mn>2</mn></math></p><p>Now, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pOH</mi><mo>=</mo><mo>-</mo><mi>log</mi><mfenced close="]" open="["><msup><mi>OH</mi><mo>-</mo></msup></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mn>2</mn><mo>=</mo><mo>-</mo><mi>log</mi><mfenced close="]" open="["><mi>OH</mi></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><msup><mi>OH</mi><mo>-</mo></msup></mfenced><mo>=</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mi mathvariant="normal">M</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mrow><mi>Ba</mi><msub><mfenced><mi>OH</mi></mfenced><mn>2</mn></msub><mfenced><mi mathvariant="normal">s</mi></mfenced></mrow><mrow><mi mathvariant="normal">S</mi><mo> </mo><mi>mol</mi><mo> </mo><msup><mi mathvariant="normal">L</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></munder><mo>⇌</mo><munder><msup><mi>Ba</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mi mathvariant="normal">S</mi></munder><mo>+</mo><munder><mrow><mn>2</mn><msup><mi>OH</mi><mo>-</mo></msup></mrow><mrow><mn>2</mn><mi mathvariant="normal">S</mi></mrow></munder></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><msup><mi>OH</mi><mo>-</mo></msup></mfenced><mo>=</mo><mn>2</mn><mi mathvariant="normal">S</mi><mo>=</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mi mathvariant="normal">M</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi mathvariant="normal">S</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>=</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">M</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mi>sp</mi></msub><mo>=</mo><mfenced close="]" open="["><msup><mi>Ba</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></mfenced><msup><mfenced close="]" open="["><msup><mi>OH</mi><mo>-</mo></msup></mfenced><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo>(</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>)</mo><msup><mrow><mo>(</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow><mn>2</mn></msup><mo>=</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup><msup><mi mathvariant="normal">M</mi><mn>3</mn></msup></math></p><p>Therefore, the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><msub><mi mathvariant="normal">K</mi><mi>sp</mi></msub></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">M</mi><mn>3</mn></msup></math>.</p></div>


title: phosphate-pollution-is-caused-by
slug: phosphate-pollution-is-caused-by-96837
question: <div class="question">Phosphate pollution is caused by:</div>
tags: ['Chemistry', 'Environmental Chemistry', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">Phosphate pollution is caused by sewage and agricultural fertilizers.</div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Sewage and agricultural fertilizers.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Weathering of phosphate rocks only.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad$ Agriculutral fertilizers only.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Phosphate rocks and sewage.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Sewage and agricultural fertilizers.</span> </div>


title: phosphine-is-not-obtained-by-the-reaction
slug: phosphine-is-not-obtained-by-the-reaction-96802
question: <div class="question">Phosphine is not obtained by the reaction</div>
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'BITSAT', 'BITSAT 2011']
answer: <div class="solution">Red P does not react with $\mathrm{NaOH}$ to give<br/>$\mathrm{PH}_{3}$</div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">White $P$ is heated with $\mathrm{NaOH}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\operatorname{Red} P$ is heated with $\mathrm{NaOH}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Ca}_{3} \mathrm{P}_{2}$ reacts with water</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Phosphorus trioxide is boiled with water</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\operatorname{Red} P$ is heated with $\mathrm{NaOH}$</span> </div>


title: phosphine-is-not-obtained-by-which-of-the-following-reaction
slug: phosphine-is-not-obtained-by-which-of-the-following-reaction-97272
question: <div class="question">Phosphine is not obtained by which of the following reaction?</div>
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'BITSAT', 'BITSAT 2020']
answer: <div class="solution">Red P doesnot react with $\mathrm{NaOH}$ to give $\mathrm{PH}_{3}$.</div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">White $\mathrm{P}$ is heated with $\mathrm{NaOH}$.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Red P is heated with $\mathrm{NaOH}$.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Ca}_{3} \mathrm{P}_{2}$ reacts with water.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Both (a) and (c).</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Red P is heated with $\mathrm{NaOH}$.</span> </div>


title: photochemical-smog-formed-in-congested-metropolitan-cities-mainly-consists-of-1
slug: photochemical-smog-formed-in-congested-metropolitan-cities-mainly-consists-of-1-97333
tags: ['Chemistry', 'Environmental Chemistry', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">Photochemical smog formed in congested metropolitan cities mainly consists of</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>ozone, peroxyacetyl nitrate and $\mathrm{NO}_x$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>smoke, peroxyacetyl nitrate and $\mathrm{SO}_2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>hydrocarbons, $\mathrm{SO}_2$ and $\mathrm{CO}_2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>hydrocarbons, ozone and $\mathrm{SO}_x$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>ozone, peroxyacetyl nitrate and $\mathrm{NO}_x$</span> </div>

answer:
<div class="solution">Photochemical smog $\Rightarrow \mathrm{O}_3, \mathrm{PAN}, \mathrm{NO}_x$</div>


tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch2_P2.db
title:
plots-showing-the-variation-of-the-rate-constant-k-with-temperature-t-are-given-below-the-plot-that-follows-arrhenius-equation-is-1

slug:
plots-showing-the-variation-of-the-rate-constant-k-with-temperature-t-are-given-below-the-plot-that-follows-arrhenius-equation-is-1-48331

question:
<div class="question">Plots showing the variation of the rate constant $(k)$ with temperature $(T)$ are given below. The plot that follows Arrhenius equation is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/UI1ku2Zk2d354YwkG7GmQJgMOdYj21cDLFCptJbFmN0.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/GVkb-vJVSZbyzoBOjEphQV0yPTuwQbdzewYcqDkBplk.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/fyskVUDKzX0giXROWygkrR0T0D8UaUY2PhitraFaQ5Q.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6GOcw__PmD0UXumjzxQSL2HTv2eYlFCrv08wbLz17d8.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/UI1ku2Zk2d354YwkG7GmQJgMOdYj21cDLFCptJbFmN0.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">As per Arrhenius equation $\left(k=A \mathrm{e}^{-E_a / R T}\right)$, the rate constant increases exponentially with temperature.</div>


title: point-out-the-false-statement-1
slug: point-out-the-false-statement-1-45333
question: <div class="question">Point out the false statement :</div>
tags: ['Chemistry', 'Surface Chemistry', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>The colloidal solution of a liquid in liquid is called gel</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Hardy Schulze rule is related with coagulation</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Brownian movement and Tyndall effect are shown by colloidal system</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Gold number is a measure of the protective power of lyophilic colloid</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>The colloidal solution of a liquid in liquid is called gel</span> </div>

answer:
<div class="solution">Colloid of liquid in liquid is called emulsion. Colloid of liquid in solid is gel.</div>


title: polymer-used-in-bullet-proof-glass-is
slug: polymer-used-in-bullet-proof-glass-is-79093
question: <div class="question">Polymer used in bullet proof glass is</div>
tags: ['Chemistry', 'Polymers', 'BITSAT', 'BITSAT 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">PMMA</span> </div>
answer: <div class="solution">PMMA is used in bullet proof glass</div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Lexan</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">PMMA</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Nomex</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Kevlar</span> </li> </ul>


title: position-of-nonpolar-and-polar-part-in-micelle-is
slug: position-of-nonpolar-and-polar-part-in-micelle-is-36287
question: <div class="question">Position of non-polar and polar part in micelle is</div>
tags: ['Chemistry', 'Surface Chemistry', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">polar at outer surface and non-polar at inner surface.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">polar at inner surface and non-polar at outer surface.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">distributed all over the surface.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">present in the surface only.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">polar at outer surface and non-polar at inner surface.</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/lDb_PcltkjfAeQ7fzTl81Pma71V5iPzM9WpFVc4M9vE.original.fullsize.png"/></div>


tags: ['Mathematics', 'Basic of Mathematics', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P2.db
title:
prabhat-wants-to-invest-the-total-amount-of-r-s-15-000-in-saving-certificates-and-national-saving-bonds-according-to-rules-he-has-to-invest-at-least-r

slug:
prabhat-wants-to-invest-the-total-amount-of-r-s-15-000-in-saving-certificates-and-national-saving-bonds-according-to-rules-he-has-to-invest-at-least-r-43464

question:
<div class="question">Prabhat wants to invest the total amount of $Rs 15,000$ in saving certificates and national saving bonds. According to rules, he has to invest at least $Rs 2000$ in saving certificates and $Rs 2500$ in national saving bonds. The interest rate is $8 \%$ on saving certificate and $10 \%$ on national saving bonds per annum. He invest $Rs$ x in saving certificate and $Rs$ y in national saving bonds. Then the objective function for this problem is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.08 \mathrm{x}+0.10 \mathrm{y}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{x}{2000}+\frac{y}{2500}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2000 \mathrm{x}+2500 \mathrm{y}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{x}{8}+\frac{y}{10}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.08 \mathrm{x}+0.10 \mathrm{y}$</span> </div>

answer:
<div class="solution">The function is given by profit function
<br/>$$
<br/>=x \cdot \frac{8}{100}+y \times \frac{10}{100}=0.08+0.10 y .
<br/>$$</div>


title: primary-amines-can-be-distinguished-from-secondary-and-tertiary-amines-by-reacting-with
slug: primary-amines-can-be-distinguished-from-secondary-and-tertiary-amines-by-reacting-with-58394
tags: ['Chemistry', 'Amines', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">Primary amines can be distinguished from secondary and tertiary amines by reacting with</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Chloroform and alcoholic $\mathrm{KOH}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Methyl iodide</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Chloroform alone</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Zinc Dust</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Chloroform and alcoholic $\mathrm{KOH}$</span> </div>

answer:
<div class="solution">$1^{\circ}$ amines (aliphatic and aromatic) react with $\mathrm{CHCl}_3 / \mathrm{KOH}$ to yield isocyanide (foul smelling) This is known as carbylamine test which is not given by $2^{\circ}$ and $3^{\circ}$ amines.</div>


title: product-d-in-above-reaction-is
slug: product-d-in-above-reaction-is-56793
tags: ['Chemistry', 'Aldehydes and Ketones', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch2_P2.db
question:
<div class="question"><img src="  data:image/png;base64,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"/> <br/>Product (D) in above reaction is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6j7t2KA5sOU2ZXI_I1dYJWOyq1t4qHVjQ1UTjB6TnLk.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/PV2IKtRy8ZmFhezwCL2ghQBU58KSH_O15xMFGtkJXH8.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/on7Y4dMW2dxg4siy_ZtC_adufx2mYm6TONJnkw4lIsI.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/9u9hkURj336HFDLz2zD9yNN6Yj-MGAmBy7X-q4BNOyw.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/PV2IKtRy8ZmFhezwCL2ghQBU58KSH_O15xMFGtkJXH8.original.fullsize.png"/></span> </div>

answer:
<div class="solution">(A) <img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/nKIJMjbU_cLHkk4796dwy8cRZG57K_n4QBGC41XD2FU.original.fullsize.png"/><br/> <br/> <br/>(B) <img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/azBZzPfS1JHXwcD9ABkHpgJYb7ldn74REp-qKH0Ykl4.original.fullsize.png"/><br/> <br/> <br/>(C) <img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/vyYpI_WL7qkkJFCTNlCPxk9VwGwZXg71d0cIBmF2bDc.original.fullsize.png"/><br/> <br/> <br/>(D) <img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ULc32EX86Mu-AEh1rEfqxyDvjPFkGeFtvhIu79t0oJ0.original.fullsize.png"/></div>


tags: ['Physics', 'Dual Nature of Matter', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1: 1$</span> </div>
source_db: MarksBatch2_P2.db
title:
proton-p-and-electron-e-will-have-same-debroglie-wavelength-when-the-ratio-of-their-momentum-is-assume-m-p-1849-m-e-1

slug:
proton-p-and-electron-e-will-have-same-debroglie-wavelength-when-the-ratio-of-their-momentum-is-assume-m-p-1849-m-e-1-74397

question:
<div class="question">Proton (p) and electron (e) will have same deBroglie wavelength when the ratio of their momentum is (assume, $m_p=1849 \mathrm{~m}_{\mathrm{e}}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1: 43$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$43: 1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1: 1849$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$1: 1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">De Broglie wavelength is $\lambda=\frac{\mathrm{h}}{\mathrm{mv}}$<br/>$\lambda_{\mathrm{p}}=\lambda_{\mathrm{e}} \Rightarrow \frac{\mathrm{h}}{\mathrm{m}_{\mathrm{p}} \mathrm{v}_{\mathrm{p}}}=\frac{\mathrm{h}}{\mathrm{m}_{\mathrm{e}} \mathrm{v}_{\mathrm{e}}}$<br/>$\mathrm{m}_{\mathrm{e}} \mathrm{v}_{\mathrm{e}}=\mathrm{m}_{\mathrm{p}} \mathrm{v}_{\mathrm{p}} \Rightarrow \mathrm{p}_{\mathrm{e}}=\mathrm{p}_{\mathrm{p}}$<br/>$\therefore \frac{\mathrm{p}_{\mathrm{p}}}{\mathrm{p}_{\mathrm{e}}}=\frac{1}{1}$</div>


tags: ['Mathematics', 'Circle', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
radius-of-the-largest-circle-which-passes-through-the-focus-of-the-parabola-y-2-4-x-and-contained-in-it-is-1

slug:
radius-of-the-largest-circle-which-passes-through-the-focus-of-the-parabola-y-2-4-x-and-contained-in-it-is-1-80880

question:
<div class="question">Radius of the largest circle which passes through the focus of the parabola <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn><mi>x</mi></math> and contained in it, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></span> </div>

answer:
<div class="solution"><p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> be the radius of the largest circle passing through the focus <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn><mi>x</mi></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/807de1a8-d722-452e-8c32-2df7ef662bcd-d48.png" style="width: 325px; height: 250px;"/></p><p>Clearly, centre of the circle will be on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>-axis and its coordinates are <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>+</mo><mi>r</mi><mo>,</mo><mn>0</mn></mrow></mfenced></math>.</p><p>The equation of the circle, is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn><mo>-</mo><mi>r</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><msup><mi>r</mi><mn>2</mn></msup></math>.</p><p>It touches <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn><mi>x</mi></math>. Therefore, the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>r</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>=</mo><msup><mi>r</mi><mn>2</mn></msup></math> must have equal roots.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mn>4</mn><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>r</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mfenced><mrow><mn>2</mn><mi>r</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>r</mi><mo>=</mo><mn>4</mn></math></p><p>Hence, option (b) is correct.</p></div>


tags: ['Mathematics', 'Circle', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P2.db
title:
radius-of-the-largest-circle-which-passes-through-the-focus-of-the-parabola-y-2-4-x-and-contained-in-it-is

slug:
radius-of-the-largest-circle-which-passes-through-the-focus-of-the-parabola-y-2-4-x-and-contained-in-it-is-82500

question:
<div class="question">Radius of the largest circle which passes through the focus of the parabola <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn><mi>x</mi></math> and contained in it, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></span> </div>

answer:
<div class="solution"><p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> be the radius of the largest circle passing through the focus <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn><mi>x</mi></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/807de1a8-d722-452e-8c32-2df7ef662bcd-d48.png" style="width: 325px; height: 250px;"/></p><p>Clearly, centre of the circle will be on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>-axis and its coordinates are <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>+</mo><mi>r</mi><mo>,</mo><mn>0</mn></mrow></mfenced></math>.</p><p>The equation of the circle, is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn><mo>-</mo><mi>r</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><msup><mi>r</mi><mn>2</mn></msup></math>.</p><p>It touches <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn><mi>x</mi></math>. Therefore, the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>r</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>=</mo><msup><mi>r</mi><mn>2</mn></msup></math> must have equal roots.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mn>4</mn><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>r</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mfenced><mrow><mn>2</mn><mi>r</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>r</mi><mo>=</mo><mn>4</mn></math></p><p>Hence, option (b) is correct.</p></div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P2.db
title:
ratio-of-thermal-energy-released-in-two-resistor-r-and-3-r-connected-in-parallel-in-an-electric-circuit-is-1

slug:
ratio-of-thermal-energy-released-in-two-resistor-r-and-3-r-connected-in-parallel-in-an-electric-circuit-is-1-86519

question:
<div class="question">Ratio of thermal energy released in two resistor $R$ and $3 R$ connected in parallel in an electric circuit is :</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>3 : 1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>1 : 1</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>1 : 3</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>1 : 27</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>3 : 1</span> </div>

answer:
<div class="solution">Thermal energy is given by<br/>$\mathrm{H}=\mathrm{P} \times \mathrm{t}=\frac{\mathrm{V}^2}{\mathrm{R}} \times \mathrm{t}$<br/>Here, voltage $\mathrm{V}$ is same.<br/>$\therefore \quad \frac{\mathrm{H}_1}{\mathrm{H}_2}=\frac{\frac{\mathrm{V}^2 \mathrm{t}}{\mathrm{R}}}{\frac{\mathrm{V}^2 \mathrm{t}}{3 \mathrm{R}}}=3: 1$</div>


title: reductive-ozonolysis-of-ch-3-2-c-c-ch-3-2-followed-by-hydrolysis-gives
slug: reductive-ozonolysis-of-ch-3-2-c-c-ch-3-2-followed-by-hydrolysis-gives-50513
tags: ['Chemistry', 'Hydrocarbons', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P2.db
question:
<div class="question">Reductive ozonolysis of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced><mn>2</mn></msub><mi mathvariant="normal">C</mi><mo>=</mo><mi mathvariant="normal">C</mi><msub><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced><mn>2</mn></msub></math> followed by hydrolysis gives </div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">only one type of ketone</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">only one type of aldehyde</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">two types of ketone</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">two types of aldehyde</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">only one type of ketone</span> </div>

answer:
<div class="solution"><p>Reductive ozonolysis of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced><mn>2</mn></msub><mi mathvariant="normal">C</mi><mo>=</mo><mi mathvariant="normal">C</mi><msub><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced><mn>2</mn></msub></math> followed by hydrolysis gives only one type of ketones because of symmetry across the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">C</mi><mo>=</mo><mi mathvariant="normal">C</mi></math> and bonding of two same alkyl groups <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced></math> with both the carbons bonded through double bond.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4fb0fc37-4690-463f-88d9-65f335775666-530db92e-b486-4eb8-931c-0508e71f96c5-image.png" style="width: 526px; height: 167px;"/></p></div>


title: reflection-of-the-line-x-1-1-y-2-3-z-4-1-in-the-plane-x-y-z-7-is
slug: reflection-of-the-line-x-1-1-y-2-3-z-4-1-in-the-plane-x-y-z-7-is-69971
tags: ['Mathematics', 'Three Dimensional Geometry', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch2_P2.db
question:
<div class="question">Reflection of the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mn>2</mn></mrow><mn>3</mn></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>-</mo><mn>4</mn></mrow><mn>1</mn></mfrac></math> in the plane <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>7</mn></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mn>3</mn></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mn>2</mn></mrow><mn>1</mn></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>-</mo><mn>4</mn></mrow><mn>1</mn></mfrac></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mn>2</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>-</mo><mn>4</mn></mrow><mn>1</mn></mfrac></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mn>2</mn></mrow><mn>1</mn></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>-</mo><mn>4</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mn>3</mn></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mn>2</mn></mrow><mn>1</mn></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>-</mo><mn>4</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mn>2</mn></mrow><mn>1</mn></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>-</mo><mn>4</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac></math></span> </div>

answer:
<div class="solution"><p>Given line <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mn>2</mn></mrow><mn>3</mn></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>-</mo><mn>4</mn></mrow><mn>1</mn></mfrac></math> is passes through <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math>.</p><p>To find the reflection of line we need one more point on the line clearly <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math> also lie on line.</p><p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>)</mo></math> be the reflection <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>7</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mfrac><mi>α</mi><mn>2</mn></mfrac><mo>+</mo><mfrac><mrow><mi>β</mi><mo>+</mo><mn>5</mn></mrow><mn>2</mn></mfrac><mo>+</mo><mfrac><mrow><mi>γ</mi><mo>+</mo><mn>5</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mn>7</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>+</mo><mi>γ</mi><mo>=</mo><mn>4</mn></math></p><p>Also, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>N</mi></math> is perpendicular, i.e. parallel to the normal of the plane</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mfrac><mi>α</mi><mn>1</mn></mfrac><mo>=</mo><mfrac><mrow><mi>β</mi><mo>-</mo><mn>5</mn></mrow><mn>1</mn></mfrac><mo>=</mo><mfrac><mrow><mi>γ</mi><mo>-</mo><mn>5</mn></mrow><mn>1</mn></mfrac><mo>=</mo><mi>λ</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>α</mi><mo>=</mo><mi>λ</mi><mo>,</mo><mi>β</mi><mo>=</mo><mi>λ</mi><mo>+</mo><mn>5</mn><mo>,</mo><mi>γ</mi><mo>=</mo><mi>λ</mi><mo>+</mo><mn>5</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>λ</mi><mo>+</mo><mi>λ</mi><mo>+</mo><mn>5</mn><mo>+</mo><mi>λ</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>4</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>λ</mi><mo>=</mo><mo>-</mo><mn>2</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>N</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></p><p>Equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>N</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mn>2</mn></mrow><mn>1</mn></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>-</mo><mn>4</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac></math></p></div>


title: resolving-power-of-the-telescope-will-be-more-if-the-diameter-of-the-objective-is
slug: resolving-power-of-the-telescope-will-be-more-if-the-diameter-of-the-objective-is-58986
tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">larger</span> </div>
answer: <div class="solution">No Solution</div>
source_db: MarksBatch2_P2.db
question:
<div class="question">Resolving power of the telescope will be more, if the diameter of the objective is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">larger</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">smaller</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">it does not depends on diameter</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>


title: rolles-theorem-is-not-applicable-for-the-function-f-x-x-in-the-interval-1-1-because
slug: rolles-theorem-is-not-applicable-for-the-function-f-x-x-in-the-interval-1-1-because-73519
tags: ['Mathematics', 'Application of Derivatives', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P2.db
question:
<div class="question">Rolle's theorem is not applicable for the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>|</mo><mi>x</mi><mo>|</mo></math> in the interval <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></math> because</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mn>1</mn><mo>)</mo></math> does not exist</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></math> does not exist</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> is discontinuous at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mn>0</mn><mo>)</mo></math> does not exist</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mn>0</mn><mo>)</mo></math> does not exist</span> </div>

answer:
<div class="solution"><p>We have,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>|</mo><mi>x</mi><mo>|</mo></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ffce6ca3-49aa-4259-a0a0-8ee87b381d58-image.png" style="width: 250px; height: 190px;"/></p><p>We know that the function is not differentiable at the sharp edges. Hence, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is not differentiable at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math>.  Therefore, Rolle's theorem is not applicable for the function</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>|</mo><mi>x</mi><mo>|</mo></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mn>0</mn><mo>)</mo></math> does not exist.</p></div>


tags: ['Mathematics', 'Ellipse', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
s-and-t-are-the-foci-of-an-ellipse-and-b-is-an-end-of-the-minor-axis-if-stb-is-an-equilateral-triangle-then-the-eccentricity-of-the-ellipse-is-1

slug:
s-and-t-are-the-foci-of-an-ellipse-and-b-is-an-end-of-the-minor-axis-if-stb-is-an-equilateral-triangle-then-the-eccentricity-of-the-ellipse-is-1-84306

question:
<div class="question">$\mathrm{S}$ and $\mathrm{T}$ are the foci of an ellipse and $\mathrm{B}$ is an end of the minor axis. If STB is an equilateral triangle, then the eccentricity of the ellipse is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2}{3}$</span> </li> </ul>

answer:
<div class="solution">Let eq. of ellipse be $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, $\mathrm{S}$ is $(-\mathrm{ae}, 0), \mathrm{T}$ is $(\mathrm{ae}, 0)$ and $\mathrm{B}$ is $(0, \mathrm{~b})$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/oOGjD6NyVDk2FaWoimoG2G8B4w4uebxeLD-nKEOVzGg.original.fullsize.png"/><br/> <br/> <br/>$\Rightarrow \mathrm{SB}=\sqrt{(0+\mathrm{ae})^{2}+\mathrm{b}^{2}}$
<br/> <br/>Also $\mathrm{SB}^{2}=\mathrm{ST}^{2} \Rightarrow 4 \mathrm{a}^{2} \mathrm{e}^{2}=\mathrm{a}^{2} \mathrm{e}^{2}+\mathrm{b}^{2}$
<br/> <br/>$\Rightarrow 3 a^{2} e^{2}=a^{2}\left(1-e^{2}\right)=a^{2}-a^{2} e^{2}$
<br/> <br/>$\Rightarrow 4 a^{2} e^{2}=a^{2} \Rightarrow e^{2}=\frac{1}{4} \Rightarrow e=\frac{1}{2}$</div>


tags: ['Mathematics', 'Ellipse', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P2.db
title:
s-and-t-are-the-foci-of-an-ellipse-and-b-is-an-end-of-the-minor-axis-if-stb-is-an-equilateral-triangle-then-the-eccentricity-of-the-ellipse-is

slug:
s-and-t-are-the-foci-of-an-ellipse-and-b-is-an-end-of-the-minor-axis-if-stb-is-an-equilateral-triangle-then-the-eccentricity-of-the-ellipse-is-52765

question:
<div class="question">$\mathrm{S}$ and $\mathrm{T}$ are the foci of an ellipse and $\mathrm{B}$ is an end of the minor axis. If STB is an equilateral triangle, then the eccentricity of the ellipse is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2}{3}$</span> </li> </ul>

answer:
<div class="solution">Let eq. of ellipse be $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, $\mathrm{S}$ is $(-\mathrm{ae}, 0), \mathrm{T}$ is $(\mathrm{ae}, 0)$ and $\mathrm{B}$ is $(0, \mathrm{~b})$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/oOGjD6NyVDk2FaWoimoG2G8B4w4uebxeLD-nKEOVzGg.original.fullsize.png"/><br/> <br/> <br/>$\Rightarrow \mathrm{SB}=\sqrt{(0+\mathrm{ae})^{2}+\mathrm{b}^{2}}$
<br/> <br/>Also $\mathrm{SB}^{2}=\mathrm{ST}^{2} \Rightarrow 4 \mathrm{a}^{2} \mathrm{e}^{2}=\mathrm{a}^{2} \mathrm{e}^{2}+\mathrm{b}^{2}$
<br/> <br/>$\Rightarrow 3 a^{2} e^{2}=a^{2}\left(1-e^{2}\right)=a^{2}-a^{2} e^{2}$
<br/> <br/>$\Rightarrow 4 a^{2} e^{2}=a^{2} \Rightarrow e^{2}=\frac{1}{4} \Rightarrow e=\frac{1}{2}$</div>


title: s-s-bond-is-not-present-in
slug: s-s-bond-is-not-present-in-78869
question: <div class="question">$\mathrm{S}-\mathrm{S}$ bond is not present in</div>
source_db: MarksBatch2_P2.db
tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{S}_2 \mathrm{O}_4^{2-}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{S}_2 \mathrm{O}_5^{2-}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{S}_2 \mathrm{O}_3^{2-}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{S}_2 \mathrm{O}_7^{2-}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{S}_2 \mathrm{O}_7^{2-}$</span> </div>

answer:
<div class="solution">$\mathrm{S}_2 \mathrm{O}_7^{2-}$ has  $\mathrm{S}-\mathrm{O}-\mathrm{S}$ bond.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/-CKmAGRwM3ThbB8zyZlo7Z8MvD8Muyz0dSpKgRJh5Rc.original.fullsize.png"/><br/></div>


title: schottenbaumann-reaction-is-a-reaction-of-phenols-with-1
slug: schottenbaumann-reaction-is-a-reaction-of-phenols-with-1-53512
question: <div class="question">Schotten-Baumann reaction is a reaction of phenols with</div>
tags: ['Chemistry', 'Amines', 'JEE Main']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">benzoyl chloride and sodium hydroxide.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">acetyl chloride and sodium hydroxide.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">salicylic acid and conc. $\mathrm{H}_{2} \mathrm{SO}_{4}$.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">acetyl chloride and conc $\mathrm{H}_{2} \mathrm{SO}_{4}$.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">benzoyl chloride and sodium hydroxide.</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/WBj_lWT234eV9FqLu0bDtcEjrjKE21EKAVHbwLeMJ6g.original.fullsize.png"/><br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Cnjcx-Cwfm0WM4lOCaNK6DQW2O1AjgJAYWoBR4q05dE.original.fullsize.png"/></div>


title: select-the-correct-statement-about-the-complex-co-nh-3-5-so-4-br
slug: select-the-correct-statement-about-the-complex-co-nh-3-5-so-4-br-17905
tags: ['Chemistry', 'Coordination Compounds', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P2.db
question:
<div class="question">Select the correct statement about the complex
<br/>$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{SO}_4\right] \mathrm{Br}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>Its ionisation isomer is $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Br}\right] \mathrm{SO}_4$.
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>It gives yellow precipitate with $\mathrm{AgNO}_3$.
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>Its ionisation isomer give while precipitate with $\mathrm{BaCl}_2$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>All the above are correct statements.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>All the above are correct statements.</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/UGHrZBe_j7OY0Ci6VlgJA61s8XKmHcpyVsfbq698xIc.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/mpsL_7-9mRm24R4XN74Ege9AE3tgSCT43oR-6z39pRE.original.fullsize.png"/><br/></div>


title: select-the-incorrect-statement-57
slug: select-the-incorrect-statement-57-57702
question: <div class="question">Select the incorrect statement.</div>
tags: ['Chemistry', 'Chemistry in Everyday Life', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Equanil is used to control depression and hypertension.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Mifepristone is a synthetic steroid used as "moming after pill".</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0.2 per cent solution of phenol is an antiseptic while its 1.0 per cent solution is a disinfectant.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">A drug which kills the organism in the body is called bacteriostatic.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A drug which kills the organism in the body is called bacteriostatic.</span> </div>

answer:
<div class="solution">Bacteriostatic drugs inhibit the growth of organisms while bactericidal drugs kill the microorganisms.</div>


title: semiconductor-materials-like-si-and-ge-are-usually-purified-by
slug: semiconductor-materials-like-si-and-ge-are-usually-purified-by-31675
question: <div class="question">Semiconductor materials like Si and Ge are usually purified by</div>
tags: ['Chemistry', 'General Principles and Processes of Isolation of Metals', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">distillation</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">zone refining</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">liquation</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">electrolytic refining</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">zone refining</span> </div>

answer:
<div class="solution">Semiconductor materials like Si and Ge are usually purified by zone refining. Zone refining is based on the principle of fractional crystallisation i.e. difference in
<br/> <br/>states of metal, so that the zones of impurities are formed and finally removed.</div>


title: sodium-nitroprusside-when-added-to-an-alkaline-solution-of-sulphide-ions-produce-a
slug: sodium-nitroprusside-when-added-to-an-alkaline-solution-of-sulphide-ions-produce-a-33989
tags: ['Chemistry', 'Practical Chemistry', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch2_P2.db
question:
<div class="question">Sodium nitroprusside, when added to an alkaline solution of sulphide ions, produce a</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">red colouration</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">blue colouration</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">purple colouration</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">brown colouration</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">purple colouration</span> </div>

answer:
<div class="solution"><p>This test is used for the presence of sulphur in any compound. When sodium nitroprusside, react with sulphide ion, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi mathvariant="normal">e</mi><mo>.</mo><mi mathvariant="normal">g</mi><mo>.</mo><msub><mi>Na</mi><mn>2</mn></msub><mo> </mo><mi mathvariant="normal">S</mi></mrow></mfenced></math> the following reaction takes place</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><msub><mi>Na</mi><mn>2</mn></msub><mi mathvariant="normal">S</mi><mo>+</mo><msub><mi>Na</mi><mn>2</mn></msub><mfenced close="]" open="["><mrow><mi>Fe</mi><msub><mfenced><mi>CN</mi></mfenced><mn>5</mn></msub><mi>NO</mi></mrow></mfenced></mtd><mtd><mo>⟶</mo></mtd><mtd><msub><mi>Na</mi><mn>4</mn></msub><mfenced close="]" open="["><mrow><mi>Fe</mi><msub><mfenced><mi>CN</mi></mfenced><mn>5</mn></msub><msub><mi>NO</mi><mn>5</mn></msub></mrow></mfenced></mtd></mtr><mtr><mtd><mfenced><mrow><mi>Sod</mi><mo>.</mo><mo> </mo><mi>nitroprusside</mi></mrow></mfenced></mtd><mtd><mo> </mo></mtd><mtd><mi>purple</mi><mo> </mo><mi>coloration</mi><mo> </mo><mfenced><mrow><mi>sod</mi><mo>.</mo><mo> </mo><mi>thionitroprusside</mi></mrow></mfenced></mtd></mtr></mtable></math></p></div>


title: sodium-peroxide-in-contact-with-moist-air-turns-white-due-to-formation-of
slug: sodium-peroxide-in-contact-with-moist-air-turns-white-due-to-formation-of-84942
tags: ['Chemistry', 's Block Elements', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch2_P2.db
question:
<div class="question">Sodium peroxide in contact with moist air turns white due to formation of:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Na}_{2} \mathrm{CO}_{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Na}_{2} \mathrm{O}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{NaOH}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{NaHCO}_{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{NaOH}$</span> </div>

answer:
<div class="solution">$\mathrm{Na}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow 2 \mathrm{NaOH}+\frac{1}{2} \mathrm{O}_{2}$</div>


title: sodium-sulphate-is-soluble-in-water-but-barium-sulphate-is-insoluble-because
slug: sodium-sulphate-is-soluble-in-water-but-barium-sulphate-is-insoluble-because-45493
tags: ['Chemistry', 's Block Elements', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P2.db
question:
<div class="question">Sodium sulphate is soluble in water but barium sulphate is insoluble because</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">hydration energy of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Na</mi><mn>2</mn></msub><msub><mi>SO</mi><mn>4</mn></msub></math> is more than of its lattice energy</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">lattice energy of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>BaSO</mi><mn>4</mn></msub></math> is more than its hydration energy</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Both <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">a</mi><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">b</mi><mo>)</mo></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">a</mi><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">b</mi><mo>)</mo></math></span> </div>

answer:
<div class="solution"><p>For any solution to become soluble in water hydration energy of the solution should me more than its lattice energy. Here the hydration energy of sodium sulphate is more than lattice energy but in case of barium sulphate lattice energy of barium sulphate is more than its hydration energy.  </p><p>For dissolution hydration energy must be more higher <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>-</mo><mi>ve</mi><mo>)</mo></math> value than of lattice energy. Thus, (c) is the correct answer.</p></div>


